chapter 9: mechanical properties of fluids Flashcards
What is pressure?
Pressure (p) at every point is defined as normal force per unit area.
p = dF / dA
unit: Pa = 1 N/m^2
Fluid force ALWAYS acts perpendicular to surface. Therefore, pressure is only scalar.
- Pressure has no particular direction
- Pressure is scalar quantity
- Pressure at a static fluid is equal in all directions
- Pressure in a fluid at rest is the same at all points if they are at same height.
Pressure at two points within the same level or horizontal plane means…
The fluid is at rest or moving with constant velocity.
Pressure at two points separated by depth separation of h when vessel is stationary means…
The fluid is at constant velocity under the expression:
p2 - p1 = ρgh, where ρ is the density of liquid (rho).
Pressure at two points ina horizontal plane when fluid container is having some constant horizontal acceleration means…
Fluid is having constant horizontal acceleration is expressed as:
p1 - p2 = = lρa , where l is the distance between two points.
and tan θ = a/g, where θ is the angle which the liquid’s free surface is making with horizontal.
Pressure at two points where theres a separation by h when the liquid container is accelerating up means…
Expression for accelerating up:
p2 - p1 = ρ ( g + a ) h
Expression for accelerating downwards:
p2 - p1 = ρ ( g - a ) h
What is atmospheric pressure and value of 1atm at sea level? The term that’s used for excess & total pressure and the device used to measure atmospheric pressure.
It is the pressure of the earth’s atmosphere. Normal atmospheric pressure at sea level is 1 (atm) = 1.013 × 10^5 Pa.
P = hρg
GAUGE PRESSURE: The excess pressure above atomospheric pressure.
ABSOLUTE PRESSURE: The total pressure
Barometer is the device to measure atmospheric pressure. U–tube manometer is a device used to measure the gauge pressure.
Define Pascal’s Law.
The change in presssure (external pressure) applied to a confined container is transmitted undiminished to every point of the fluid and the walls of the containing vessel.
What is Archimedes principle?
When a body is partially or fully dipped into a fluid, the fluid exerts contact force on the body. The resulatant of all these contact forces is called buoyant force (upthrust).
F = Vσg
where, v = volume of liquid displaced
σ = density of liquid
F = weight of fluid displaced by body
Apparent decrease in weight of body = upthrust = weight of liquid displaced by the body.
What are the three key aspects of Flotation?
- Body floats if average density of body is lower than density of liquid.
- The weight of the liquid displaced by the immersed part of body must be equal to the weight of body
- The center of buoyancy & gravity of the body must follow a vertical line.
Define Streamline flow. (steady flow) and Line of flow.
STREAMLINE FLOW: The flow in which the velocity of fluid particles crossing a particular point is the same at all the times. Thus, each particle follows the same line as the previous particle.
LINE OF FLOW: The path taken by a particle flowing in a liquid. Two streamlines can never intersect.
What is the Equation of continuity?
In a time Δt, the volume of liquid entering the tube of flow in a steady flow is A1 V1 Δt. The same volume must flow out as the liquid is incompressible. The volume flowing out in Δt is A2 V2 Δt.
A1V1 = A2V2
mass flows rate = ρAV
(where ρ is the density of the liquid.)
Define Bernoulli’s Theorem.
In a streamline flow of a fluid, the total energy ( sum of pressure energy, potential energy and kinetic energy) per unit volume is always constant at every cross-section throughout the flow.
P + ρgh + = Constant
What is a Venturi meter?
This is an instrument to measure the rate of flow of fluids.
What is Viscosity?
The property of a fluid where friction occurs between the layers of a fluid. The force that is into the play is called viscous force.
Viscous force is given by :
F = ηA dv / dx
where η is a constant depending upon the nature of the
liquid and is called the coefficient of viscosity and velocity
gradient = dv/dx
S.I. unit of coefficient of viscosity is Pa.s or Nsm^-2
CGS unit of viscocity is poise. (1 Pa.s = 10 Poise)
What is Stoke’s law?
When a solid moves through a viscous medium, its motion
is opposed by a viscous force depending on the velocity
and shape and size of the body.
The viscous drag on a spherical body of radius r, moving with
velocity v, in a viscous medium of viscosity η is given by
F viscous = 6πηrv
What is the importance of Stoke’s Law.
- Determination of electronic charge
- Accounts formation of clouds
- Helps a man coming down with the help of a parachute
Define Terminal velocity
It is maximum constant velocity acquired by the body while falling freely in a viscous medium.
v (r) = (2r^2 ( ρ - ρ0 ) g) / 9η
What is the Poiseuille’s formula.
Poiseuille studied the stream-line flow of liquid in capillary tubes. Volume of liquid coming out of tube per second in given by
= πPr^4 / 8ηl
What is Reynold’s number
R(e) = ρvD / η
ρ = the density of the fluid flowing with a speed v.
D = the diameter of the tube.
η = the coefficient of viscosity of the fluid
What is Surface tension
Tension of the surface of the particles caused by attraction by the bulk of the liquid which tends to minimise
S(t) = F/l (constant)
unit: N/m or J/m^2
What is Surface energy
It’s the energy provided on the surface in order to oppose the pull of the other molecules.
S(e) = S(t) ΔA
where ΔA = increase in surface area
What is Angle of contact?
The angle between the* tangent to the liquid surface* at the
point of contact and the solid surface inside the liquid is
called the angle of contact.
Define Capillary tube and Capillary action.
A very narrow glass tube with fine bore and open at both
ends is known as capillary tube. When a capillary tube in
dipped in a liquid, then liquid will rise or fall in the tube, this action is termed as capillarity.
To find the capillary rise:
h = 2S cosθ / rρg = 2S / Rρg
where
r - radius of capillary tube
R = radius of meniscus
θ = angle of contact
S = surface tension
ρ = density of the liquid
Explain about drops and bubbles. (Excess pressure)
The pressure inside a liquid drop is greater than the ouside. To find the excess pressure…
ΔP = P(i) - P(o)
where P(i) - internal pressure, P(o) - outer pressure
Excess pressure in a liquid bubble
P = 2T / R
