Fluid Mechanics 2 Flashcards
Flow measurement in an open channel is done by a/an
weir
Newton’s law of viscosity relates the
shear stress and rate of angular deformation in a fluid.
The equivalent diameter for fluid flow through square cross section channel of side ‘x’, for pressure drop calculation purpose is given by
x
Hydraulic radius of 6” x 12” cross-section, is __________ inches.
2
Baffles in mixing tanks are provided to
reduce swirling and vortex formation.
Which of the following equations is valid for laminar flow of a fluid through packed bed?
Kozney - Karman equation
Forces acting on a particle settling in fluid are __________ forces.
gravitational or centrifugal buoyant drag.
For a fluid rotating at constant angular velocity about vertical axis as a rigid body, the pressure intensity varies as the
square of the radial distance.
In a dry packed bed, the pressure drop will be changed by increasing the flow rate as
V^1.8
Specific speed of a centrifugal pump depends upon the __________ head.
none of these
Navier-Stokes equation is useful in the analysis of __________ fluid flow problems.
viscous
The maximum discharge through a circular channel takes place, when the depth of the fluid flow is __________ times the pipe diameter.
0.95
When the head pumped against is less than the head of the fluid used for pumping, the usual device is a/an
airlift
Two fluids are flowing through two similar pipes of the same diameter. The Reynold’s number is same. For the same flow rate if the viscosity of a fluid is reduced to half the value of the first fluid, the pressure drop will
decrease
What is the value of co-efficient of discharge for square edged circular orifice (for β = 0.3 to 0.5) ?
0.61 - 0.63
A lubricant 100 times more viscous than water would have a viscosity (in Pa.s)
0.1
Nominal Pipe Size (NPS) of a pipe less than 12 inches in diameter indicates its
neither inner nor outer diameter
I.D. of 1/4” schedule 40 pipe is 0.364”. I.D. of a 1/2” schedule 40 pipe would be __________ inch
0.5
Two liquids manometer is used for measuring small pressure differences in
gases
A piezometer provided in the pipe measures
static pressure
The pump used for irrigation purposes is generally designed for
large capacity & low head.
In centrifugal pumps, cavitation occurs, when pressure of the impeller eye or vane becomes
less than liquid vapor pressure.
Pressure gradient in the pipe flow is influenced by the
all of these
__________ pump is the most suitable device for discharging a liquid against a pressure of ≥ 1500 kgf/cm2.
Plunger
Boiler feed water pump is usually a __________ pump.
multistage centrifugal
Viscosity of a liquid decreases __________ with rise in temperature.
logarithmically
In case of a pipe of constant cross-sectional area, the maximum fluid velocity obtainable is
the velocity of sound.
Discharge in laminar flow through a pipe varies
as the square of the radius.
The lift of a ballon is
due to the weight of the atmospheric air, that it displaces.
In which of the following body shapes, the pressure drag is large compared to the friction drag ?
Bluff body
Major loss in sudden contraction in pipe flow is due to
flow contraction.
Which of the following can be used to create a flow of gas, where no significant compression is required ?
Blower
The ratio of actual discharge to theoretical discharge through an orifice is equal to
Cc . Cv
A free jet of water of cross-sectional area 0.01m^2 and a velocity of 20 m/s strikes a plate and then flows in a plane parallel to the plate as shown in the figure below. The horizontal component of the force on the support is
4000 N
Cp/Cv is termed as
adiabatic constant
Which of the following is a Newtonian fluid?
Non-colloidal solution
Which of the following valves will incur maximum pressure drop for the same discharge of water ?
Needle valve
Pressure drop in a fluidised bed reactor is __________ that in a similar packed bed reactor.
more than
In deriving Bernoulli’s equation, fluid is assumed to be
incompressible, frictionless, steady, along a streamline.
Unit of mass velocity is
kg/m^2. hr
With increase in molecular weight of the gas, the head developed by a centrifugal compressor will
decrease
Pressure difference between two points in vessels, pipelines or in two different pipelines can be measured by a differential manometer. The pressure difference measured as the mm of water coloumn in case of mercury-water, differential manometer is equal to (where, H = difference in height of mercury column in mm).
12.6 H
The boundary layer thickness at a given section along a flat plate __________ with increasing Reynold’s number.
decreases
Low specific speed of a pump implies that, it is a/an __________ pump.
centrifugal
For pumping slurry, one can use a __________ pump.
diaphargm
Bernoulli’s equation describes the
mechanical energy balance in potential flow.
Which law/principle of solid mechanics is similar/equivalent to Newton’s law of viscosity in fluid mechanics ?
Hooke’s law.
When larger particles e.g., grains are subjected to fluidisation, the corresponding bed produced is termed as the __________ bed.
spouted
Minimum fluidisation velocity for a specific system depends upon the
all of these
Potential flow is characterised by the
irrotational and frictionless flow.
For the production of very high vacuum, a __________ pump is normally used.
diffusion
In parallel pipe problems, the
head loss is the same through each pipe.
Fluid flow through a packed bed is represented by the __________ equation.
Ergun’s
__________ is an example of axial flow impeller.
Propeller
Froude number is not a factor
when there is no vortex formation.
If three pipes of different diameters, lengths & friction factors are connected in parallel, then (where, Q = flow rate, V= fluid velocity f = friction factor).
Q = Q1 + Q2 + Q3
Horsepower requirement for given pump capacity depends upon the
all of these
Bernoulli’s equation accounts for the
different forms of mechanical energy
__________ pumps are a group of vacuum pumps.
Hyter
Plunger pumps are used for
higher pressure
What is the ratio of displacement thickness to nominal thickness for a linear distribution of velocity in the boundary layer on a flat plate ?
0.5
In turbulent flow, the
shear stresses are generally larger than in a similar laminar flow.
Momentum correction factor used in fluid flow problems accounts for the
non uniform direction of velocities at inlet & outlet sections.
Design of the casing of centrifugal pump should be such as to minimise the
loss of kinetic head
Which of the following is used for pumping crude oil from oil well ?
Duplex/triplex reciprocating pump
The energy loss in flow through ven-turimeter is less than that through flow nozzle, because in case of a flow nozzle, the
sudden expansion of flow in the downstream occurs.
__________ flow means the flow of incompressible fluid with no shear.
Potential
The continuity equation
relates mass flow rate along a stream tube.
The energy loss over a length of pipeline according to Darcy-Weisbach equation for pipe flow is…..the mean velocity of flow.
directly proportional to square of
Pressure drop in a packed bed for laminar flow is given by the __________ equation.
Kozney-Karman
The fluid velocity varies as the cube of the cylinderical pipe diameter in case of steady state laminar flow at constant pressure drop for __________ fluid.
pseudoplastic
Stoke’s law is valid, when NRe, p is less than
2
Froude number is the ratio of
inertial stress to gravitational stress.
Normal depth in open channel flow is the depth of flow in the channel
corresponding to uniform flow.
Which of the following flow measuring devices is an area meter ?
Rotameter
With decrease in particle size to be fluidised by a particular fluid, the operating range of fluidisation velocity
does not change
Diaphragm valves are used for handling __________ fluids.
corrosive
The schedule number of a pipe is an indication of its
wall thickness
Minimum porosity for fluidisation is
the porosity of the bed when true fluidisation begins.
A centrifugal pump used to pump water is used to pump an oil with specific gravity of 0.8 at the same rate. The power consumption will now
decrease
Steady non-uniform flow is exemplified by flow through a/an
expanding tube at constant rate.
The maximum depth from which a centrifugal pump can draw water is
34 feet.
Hot wire anemometer is used to measure the
velocity of gases.
Propeller type centrifugal pumps are most suitable for
high capacity at low heads.
The fluid velocity varies as the square of the cylindrical pipe diameter, in case of steady state laminar flow at constant pressure drop, for __________ fluid.
Newtonion
Momentum transfer in laminar flow of fluids results due to the
velocity gradient
The capillary rise of mercury is maximum in glass tube of dia __________ mm.
0.5
Diaphragm pumps are used to transport
slurries
For steady ideal fluid flow, the Bernoulli’s equation states that the
energy is constant along a stream line, but may vary across stream lines
In case of a centrifugal pump, the theoretical head developed is dependent on the __________ the impeller.
all of these
A hydraulic press has a ram of 10 cms in diameter and a plunger of 1 cm in diameter. The force required on the plunger to raise a weight of 10 tons on the ram is __________ kg.
100
Choose the set of pressure intensities that are equivalent.
4.33 psi, 10 ft. of water, 8.83 inches of Hg.
Pick out the wrong statement about a streamline.
It is always parallel to the main direction of the fluid flow.
The most serious disadvantage of an orificemeter is that
most of the pressure drop is not recoverable.
The discharge through a rectangular weir varies as
H^3/2
In case of supersonic flow of a fluid through pipeline, the ‘Mach number’ is
> 1
A centrifugal pump has the following specifications: Power = 4 H.P.; Speed = 800 rpmHead = 8 metresFlow = 1000 litres/minutes.If its speed is halved, the power consumed now will be __________ hp.
0.5
Transition length for turbulent flow in smooth pipe is equal to __________ times the pipe diameter.
50
Disc compensators are provided in large diameter fuel gas carrying pipelines to
account for contraction/expansion of pipe due to temperature changes of the surroundings.
Discharge from a 24 inch pipe of water at 10 ft/sec will be __________ ft3/sec.
125.6
Paper pulp is an example of __________ fluid.
bingham plastic
The ratio of the depth of flow to the diameter of the channel for maximum discharge in a circular channel in open channel flow is
0.95
A conical tank with a bottom opening of cross-sectional area A is filled with water and is mounted on supports as shown in the figure. What is the force F with which plate X must be pushed up to prevent water from leaking ? Assume that the density of air is negligible as compared to the density of water ρL. (1)
ρL . A.Hg
A relief valve
is a directional control valve.
An isentropic process is the one, in which
pvr = constant, and process is reversible
The distribution of shear stress in a stream of fluid in a circular tube is
linear with radius for both laminar & turbulent flow.
For motion of spherical particles in a stationary fluid, the drag co-efficient in hindered settling compared to that in free settling is
more
Specific speed of a centrifugal pump relates it with another pump having the
dynamic similarity
Air vessel fitted to a reciprocating pump
decreases the work done.
Deformation drag, which is caused by widespread deformation of fluid around the immersed body
occurs when NRe is very small.
In isotropic turbulence, the __________ are equal to each other.
mean square of velocity fluctuations in the three co-ordinate directions
Viscosity of water is about __________ times that of air at room temperature.
55
Net positive suction head (NPSH) of a centrifugal pump must be
greater than the vapour pressure of the liquid.
Actual lift of a pump is always less than the theoretical lift and is limited by the
all of these
In case of unsteady fluid flow, conditions & flow pattern change with the passage of time at a position in a flow situation. Which of the following is an example of unsteady flow?
Water flow in the suction and discharge pipe of a reciprocating pump.
Nature of fluid flow during the opening of a valve in a pipeline is
unsteady
The __________ pressure is measured by a static tube.
static
The speed of a sound wave in a gas is analogous to the speed of
an elementary wave in an open channel.
Mercury is an ideal barometric fluid mainly due to its
very low vapor pressure.
A spherical particle is falling slow in a viscous liquid such that Reynolds number is less than 1. Which statement is correct for this situation ?
Drag, gravitational and buoyancy forces are impportant.
A gas
is a supercritical vapor.
Pitot tube measures the __________ of a fluid.
point velocity
Which of the following is not dimension-less?
Kinematic viscosity
In laminar flow through a round tube, the discharge varies
inversely as the viscosity.
Which is not a variable head meter ?
Rotameter
The pipe wall thickness is minimum for a pipe of given nominal size having schedule number
40
Reynolds number for flow of water at room temperature through 2 cm dia pipe at an average velocity of 5 cm/sec is around
1000
Centrifugal pumps as compared to reciprocating pumps
can be run with discharge line valve closed for a short interval.
What type of motion the fluid element undergoes, when it changes from one position to another position, such that the angle between the two sides change ?
Angular deformation
In which type of fluid flow, the velocity of flow of fluid changes from point to point in the fluid at any instant ?
Non-uniform
The continuity equation in ideal fluid flow states that
net rate of inflow into any small volume must be zero.
Bernoulli’s equation is not applicable, when the flow is
all of these.
The equivalent diameter for pressure drop calculation for a duct of square cross-section is given by(where, x = each side of the square duct)
x
Centre of pressure of a plane surface of arbitrary shape immersed vertically in a static mass of fluid
is independent of the specific weight of the fluid.
Drag co-efficient for flow past immersed body is the ratio of __________ to the product of velocity head and density.
average drag per unit projected area
Creeping flow around a sphere is defined, when particle Reynolds number is
< 0.1
Open channel liquid flow is most conveniently measured by a
notch
Toothpaste is a
dilatent
Slurries can be most conveniently pumped by a __________ pump.
centrifugal
Volute type of casing is provided in a centrifugal pump to
increase the discharge.
Each term of the Bernoulli’s equation written in the form, (1) , represents the total energy per unit
mass
In a free vortex, the
velocity changes linearly with radial distance.
Pick out the wrong statement.
The eddy viscosity is a fluid property.
The velocity distribution in direction normal to the direction of flow in plane Poiseuille flow is
parabolic
In fluid flow, the stagnation point is defined as a point, where the __________ is zero.
flow velocity
A special type of liquid transporting device is the diffuser pump, in which __________ are minimised.
shock losses
Which of the following is most prone to pulsating discharge flow ?
Gear pump
A streamline is
drawn normal to the velocity vector at every point.
Which of the following relationship is valid for the equilibrium position of the float in a rotameter ?(where, Df= Drag force on the float Bf = Buoyant force on the float Wf = Weight of the float)
Df + Bf = Wf
Drag is defined as the force exerted by the
fluid on the solid in the direction of flow.
The boundary layer is that part of a moving fluid, in which the fluid velocity is
affected by the presence of a solid boundary.
The terminal velocity of a solid spherical particle falling through a stationary fluid mass in the Stoke’s law range is proportional to the
all of these
Which of the following equations as suggested by Colebrook and White gives the increase in roughness of a new surface (ε0) with age/time (t) (where, ε = roughness of the surface after time’t’. α = a co-efficient to be experimentally determined)?
ε = ε0 + α.t
Nominal size of a pipe is an indication of its __________ diameter.
approximate
Fluidised beds are formed, when the
gravity force is less than the fluid friction.
A fluid is pumped at the rate of 10 lb/sec to a height of 55 ft. The horse power required is __________ hp.
1
Pick out the wrong statement:
The point at which the resultant pressure on an immersed surface acts, is known as the centre of gravity.
Medium viscosity lubricating oil can be most ideally pumped by a __________ pump.
vane
In a fully turbulent flow (Re > 105) in a pipe of diameter ‘d’, for a constant pressure gradient, the dependence of volumetric flow rate of an incompressible fluid is
d^2.5
Pump used for the transportation of molten sodium in a fast breader reactor is a/an __________ pump.
electromagnetic
Small pressure differences in liquids is measured using a/an
inclined tube manometer.
With increase in pump speed, its NPSH requirement
increases
In the Newton’s law range, the terminal velocity of a solid spherical particle falling through a stationary fluid mass is __________ the fluid viscosity.
inversely proportional to
Gear pump
is a positive displacement pump.
Most of the centrifugal pumps used in chemical plants are usually __________ driven.
electric motor
Check valve provided in the discharge line of a centrifugal pump serves the purpose of controlling the
back flow of fluid in the event of stoppage of pump.
Venturimeters, orificemeters and nozzles are used to measure the fluid discharge from a pipeline. The average fluid velocity in a pipeline can be measured by a/an
hot wire anemometer
The time taken for gravity flow of a fixed volume of liquid (as in Redwood viscometer) is directly proportional to its
ratio of absolute viscosity to density.
Sewage sludge is __________ type of non-Newtonion fluid.
Bingham plastic
Ratio of pressure and inertia force gives __________ number.
Euler
Permanent loss in a venturimeter is about __________ percent of the pressure drop in theupstream cone.
10 .
Volume of liquid displaced by a floating body is equivalent to its
own weight
The __________ is measured by a piezometric opening.
total pressure
What is the pipe called which lifts water from a reservoir to a greater height than the initial level in the supply reservoir ?
Siphon
Steady uniform flow is represented by flow through a/an
long pipe at constant rate.
Pick out the correct statement pertaining to the flow through a converging-diverging tube.
No shock wave develops in the tube when the Mach number at exit is greater than unity.
Cavitation can be prevented by
maintaining the suction head sufficiently greater than the vapour pressure.
Assuming flow to be laminar, if the diameter of the pipe is halved, then the pressure drop will
increase
Steady flow occurs, when the
conditions do not change with time at any point.
With increase in the ratio of orifice diameter to pipe diameter, the fraction of the orifice pressure differential that is permanently lost
decreases
Which of the following two quantities when same, makes one pipe system equivalent to another pipe system ?
Head & discharge
The kinetic energy correction factor for velocity distribution of laminar flow is
1.66
Priming of a centrifugal pump is done to
avoid chances of separation inside the impeller.
Bed pressure drop in an air fluidised bed of catalyst particles (ρp = 200 kg/m3, Dp = 0.05 cm) of 60 cm bed depth and bed porosity of 0.5 expressed in cm of water (manometer) is
60
For pipes that must be broken at intervals for maintenance, the connector used should be a/an
union
A fluid is the one, which
cannot remain at rest under the action of shear force.
A fluid (1) is moving at critical flow condition (NRe = 2100) through a pipe of dia 3 cms. Velocity of flow is __________ cm/sec.
7
Capillary rise of mercury in a small diameter tube is proportional to (where, d = diameter of the tube, σ = surface tension of mercury)
σ
The pressure drop per unit length of pipe incurred by a fluid ‘X’ flowing through pipe is Δp. If another fluid ‘Y’ having both the specific gravity & density just double of that of fluid ‘X’, flows through the same pipe at the same flow rate/average velocity, then the pressure drop in this case will be
2Δp
Fluid flow in a/an __________ is an example of pressure flow.
pipe
In the laminar boundary layer flow over a flat plate, the ratio (δ/x) varies as :(where, ‘δ’ is the boundary layer thickness and ‘x’ is the distance from the leading edge in the direction of flow).
Re^-1/2
A rotameter through which air at room temperature and atmospheric pressure is flowing gives a certain reading for a flow rate of 100 cc/sec. If helium (molecular weight 4) is used and rotameter shows the same reading, the flow rate (cc/sec) is
269
A 0.5 m high bed made up of a 1 mm dia glass sphere (density 2500 kg/m^3 ) is to be fluidised by water (density 1000 kg/m^3 ). If at the point of incipient fluidisation, the bed voidage is 40%, the pressure drop across the bed is
4.4 KPa
Select the wrong statement pertaining to flow of an incompressible fluid through a venturimeter.
Venturimeter occupies less space than an orificemeter.
Reynolds number for water flow through a tube of I.D. 5 cm is 1500. If a liquid of 5 centipoise viscosity and 0.8 specific gravity flows in the same pipe at the same velocity, then the pressure drop will
increase
The bulk modulus of elasticity of a liquid
increases with pressure.
Curve III in the above diagram represents a/an
pseudo plastic fluid
What is the ratio of total kinetic energy of fluid passing per second to the value obtained on the basis of average velocity (for laminar flow through a circular pipe)?
1
The line traced by a single fluid particle as it moves over a period of time is called __________ line.
path
A stream tube is that, which has __________ cross-section entirely bounded by stream lines.
any convenient
Colebrook equation for friction factor in turbulent flow is given by, (1) . It reduces to Nikuradse equation for a value of (1) equal to
1
The unit of velocity head is
ft-lbf/lb
Which of the following properties of a fluid is responsible for offering resistance to shear ?
Viscosity.
Erosion and pits formation on the impeller of a centrifugal pump may be due to
cavitation.
The velocity profile exhibited by laminar flow of Newtonion fluids is such that the velocity distribution w.r.t. radius of the circular pipe is a/an __________ with the apex at the centre line of the pipe.
parabola
The excess of the sum of pressure & velocity heads over the vapor pressure of the liquid at the suction is called the
net positive suction head (NPSH).
Piezometric head is the sum of the __________ heads.
elevation & pressure
Propellers are
axial flow mixers.
Which of the following is not an advantage of fluidisation from transfer operation point of view?
Lower fluid pumping power requirement.
Upto what value of ‘Mach number’, a fluid may be considered as incompressible ?
0.3
The head developed by a centrifugal pump is largely determined by the
angle of the vanes and the speed of the tip of the impeller.
Pick out the wrong statement:
Friction losses in pipe fittings are generally expressed in terms of velocity heads.
Flow rate of high velocity flue gas discharged through a stack to the atmosphere can be most conveniently measured by a
pitot tube
Potential flow is the flow of
incompressible fluids with no shear.
The value of critical Reynolds number for pipe flow is
1300
Mach number is important in a fluid flow problem, when the inertia and __________ forces predominate.
elastic
Fanning friction factor is equal to(where, fB = Blassius friction factor).
fB/4
In case of coutte flow, the fluid flow is between two large flat parallel plates with
top plate moving and the bottom plate fixed.
In a stabilised soap bubble, pressure inside it compared to external pressure is
more
The component of acceleration resulting due to unsteady nature of flow is called __________ acceleration.
local
Power required for mixing Newtonion fluids is a function of the
none of these.
Multistage compressors are used in industry, because they
resemble closely to isothermal compression.
The hydrodynamic and thermal boundary layers will merge, when
Prandtl number is one.
Differential manometer measures the
pressure difference between two points.
For a stable equilibrium of a submerged body (where, G and B are centres of gravity & buoyancy respectively).
B is above G
With increase in the ratio of orifice diameter to pipe diameter in case of an orificemeter, the overall pressure loss
remains constant
The vent valve provided in a liquid handling centrifugal pump is
all (a), and (b) and (c).
The discharge through a semi-circular weir varies as (where, H = Head of liquid.)
H^2
The Mach number for hypersonic flow of compressible fluid is
> 4
Boundary layer thickness in turbulent flow over a flat plate increases as(where, d = distance from the leading edge.)
d^4/5
The valve used for very remote and accurate control of fluid is a __________ valve.
needle
f = 16/NRe, is valid for
none of these
A mixed flow centrifugal pump
employs such an impeller, through which the flow is a combination of radial & axial flow.
In centrifugal pump operation, the cavitation can be eliminated by maintaining suction pressure __________ the vapor pressure of the liquid at the suction temperature.
higher than
A rectangular surface 3’ x 4’, has the lower 3 edge horizontal and 6’ below a free oil surface (sp. gr. 0.8). The surface inclination is 300 with the horizontal. The force on one side of the surface is(where, y = specific weight of water)
48y
A bed of spherical particles (specific gravity 2.5) of uniform size 1500 μm is 0.5 m in diameter and 0.5 m high. In packed bed state, the porosity may be taken as 0.4. Ergun’s equation for the above fluid-particle system (in SI units) is given below : Δ P/L = 375 x 10^3 VOM + 10.94 x 10^6 V^2OM (SI units) If water is to be used as the fluidising medium, the minimum fluidisation velocity, VOM is
16 mm/s
One dimensional flow implies
a flow which does not account for changes in transverse direction.
In case of turbulent flow of a Newtonion fluid in a straight pipe, the maximum velocity is equal to (where, Vavg = average fluid velocity)
1.2 Vavg
Centrifugal compressors compared to reciprocating compressors
all of these
For laminar flow of Newtonion fluids through a circular pipe, for a given pressure drop and length & diameter of pipe, the velocity of fluid is proportional to(where, μ = fluid viscosity )
1/μ
Umf is the minimum fluidisation velocity for a bed of particles. An increase in the superficial gas velocity from 2 Umf to 2.5 Umf results in (all velocities are smaller than the entrainment velocity of the particles) no change in the
bed height
Stoke’s law is valid, when the particle Reynolds number is
< 1
Which of the following is not a dimension-less parameter ?
Kinematic viscosity
In which of the following cases, it is possible for flow to occur from low pressure to high pressure ?
Flow through a converging section.
The blades of a centrifugal impeller are said to be curved forward, if the __________ of the motion of impeller blades.
outlet tip of a blade is towards the direction
For the same terminal conditions and fitting size, the least friction loss is incurred in a/an
union
A floating/submerged body is always stable, if its centre of gravity
lies below its centre of buoyancy.
Critical velocity in a pipe flow
increases as pipe diameter increases.
A centrifugal pump designed to pump water is employed to pump a more viscous oil. In the later case, the pump
all of these
In an incompressible flow of fluid, the fluid
density does not change with pressure & temperature.
The ratio of maximum to average velocity in case of streamline flow between parallel plates is
1.5
A weir is used to measure the large water discharge rate from a river or from an open channel. A weir is not of __________ shape.
circular
Pressure co-efficient is the ratio of pressure forces to __________ forces.
inertial
Which of the following conditions must be satisfied for lift force to be developed ?
Circulation around the body is essentially required.
The Reynolds number for an ideal fluid flow is
∞
