fluid mechanics Flashcards
What is one bar?
105 N/m2
What do shear stresses result from?
Forces applied at a tangent.
What is pascal’s law?
Pascal’s law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.
what is the pressure gradient?
dp/dz = -ρg
what is the head?
for pressure use P=ρgh to find it
Represents energy per unti weight
What is gauge pressure?
Pressure relative to the atmosphere.
Pa= 0
How does a baramometer work?
[insert photo]
atmosphereic pressure= ρgh + vapour pressure
What is the function of a manometer?
Compare pressure in a vessel to atmospheric pressure and thus find gauge pressure.
What are the limitations of the piezometer?
Can’t measure pressure less than atmospheric
Can’t be used for gases
If it is of high pressure, it would be too tall.
How does a U-tube manometer work?
Glass tube curved to give two vertical columns.
It is filled with a liquid of different density
Used to find difference in pressures.
P-Patm=ρ2h2g-ρ1h1g
What equation would you use to find pressure difference with a manometer with different diameter ends?
p1=p2 +ρgz(1+(d2/D2))
Where z is the difference in heights
where D is the larger diameter.
If D is a lot larger than d, then p1=p2 +ρgz
What is the force acting on a vertical dam?
Where does it act?
ρgBh2 / 2
Where B is length of dam
1/3 up the side of the dam
What is the no-slip condition?
When a fluid flows past a surface, the fluid adjacent to the solid moves at the same speed as the solid.
Under what conditions do you get a linear velocity gradient between a stationary and moving plate?
The gap between the plates and the velocity is relatively small.
What is the symbol and unit for shear rate?
ℽ and s-1
What is the symbol and unit for shear stress?
𝛕
N/m2
What is 𝛕 equal to?
μ*(dy/dy)
where μ is dynamic viscosity
(viscosity units = Ns/m2)
What is kinematic viscosity
Symbol: curley ν
dynamic viscosity / density
(m2/s)
How do you find shear rate?
=du/dy
Difference in speeds of plates divided by distance between them.
What is the equation for drag?
D=0.5*area*u2*density*drag coefficient
What is laminar flow?
Small deviations in fluid flow willbe damped by viscosity and it will be smooth
What is reynolds number?
interial forces / viscous forces
= ρ*u*d/ dynamic viscosity
= u*d/ kinematic viscousity
When does laminar and turbulant flow happen?
laminar when Re<2000
Turbulent when Re>4000
Though these only apply to pipes
What are the units for reynolds number?
It has none
What is Stokes law?
When flow is laminar, CD= 24/Re
For it to be laminar Re<0.1
Learn it
How do you find buoyancy?
density*volume*g
How can mass be stored in the controle volume?
A change in density
A change in controle volume size
What is the bernoulli equation?
How do you find the head with velocity?
velocity2 / 2g
What does the bernoulli equation show?
That the energy per unit weight at one point is the same at a different point.
What is is a pitot tube?
Cylindrical, open ended tube, pointing into the flow of fluid.
What is the total head to the entrance to a pitot tube?
As the velocity of fluid there is 0, it is p/ρg +z
What is stagnation pressure?
The fluid stops at a point and v falls to 0
As P +0.5*ρ*v2 +zρg needs to be conserved the pressure has to increase to P +0.5*ρ*v2
This is the stagnation pressure.
What is a different way to express the bernoulli equation?
P +0.5*ρ*v2 +zρg
What is the discharge coefficient?
for when calculated discharge is less than expected
Cd=actual / ideal
What is dynamic pressure?
The 0.5*ρ*v2 bit of the bernoulli equation
Also known as the total head
How do you find the speed of fluid in a tube with a pitot meter?
Install a pitot tube and a standpipe (pipe perpendicular to main flow) and measure the difference in height.
difference = v2/2g
What is momentum/s?
ρ*area*v2
How does conservation of momenum apply to fluids?
Momentum per second out of controle volume = momentum per second into controle volume
Express the friction factor in terms of shear stress
f=(8𝜏)/(v^2ρ)
What is the formula for the head loss in a pipe due to friction?
h=f*(L/D)*(V2/2g)
When flow is laminar, what is the expresstion for the friction factor?
64 / Re
How are local head losses found?
Local head loss = Kl*(V2/2g)
where Kl is a constant for a particular fitting
How do you find Kl when the dimeter changes alot?
Kl=(1-(A2/A1))
A1 is intial diameter and A2 final diameter
What is Ks?
The average roughness level
When is it worth considering local loses?
When the pipe is short in length, otherwise friction dwarfs it.
What is relative roughness?
Ks / diameter
How do you find power needed to maintain flow in a pipe?
Mass per second* height loss*g
A differential manometer is used to determine the pressure difference between two cross-sections A and B in a horizontal pipe in which water is flowing. The deflection of the mercury in the gauge is 0.58m. Calculate the pressure difference between sections A and B
How do you find the force due to a water jet?
Force is rate of change of momentum. The water will lose all it’s momentum, so just find the momentum of the water.
Force=density of water*area*velocity2
How do you find the force exeted by a nozzle on a fluid?
Use Bernoulli’s equation to find P1 (P2=0 and Z1-Z2 =0)
Forces to right =pressure @1 -force-pressure@2=change in momentum
=Momentum @2 -momentum @1
What is an equation for the darcy friction factor?
f=(8τ)/(ρ*v2)
How can you find the friction factor when the flow is laminar?
f=64/Re
How do you use the cole-brook white formula?
Assume f to be a certain number e.g. 0.02
Put it into LHS and RHS. If they are disimilar, use the RHS to reverse calculate and find f. Try in
What do you use the moody diagram for?
Finding the friction factor for smooth pipes, laminar flow, finiding friction facotr when you have relative roughness and Re
How would you find the pressure gradient along a pipe having found the head loss?
Use p=ρ*g*h to find pressure drop and divide by pipe length
What are the fundamental units?
Length, Mass and Time.
There are others but don’t worry about them.
What is buckingham pi theorem?
If an equation involving k variables is dimensionally homogeneous, it can be reduced to a relationship among k-r independent dimensionless groups, where r is the minimum number of basic dimensions required to describe the variables.
We will be usung L, M and T so r=3
What is force in fundamental units?
MLT-2
How many variables are in a pi term?
How do you chose them?
3 as R=3.
You can’t use the independent varaible e.g. what you are trying to find
You can’t use things with the same units e.g. length, area and volume.
What are forces at terminal velocity?
weight-drag-bouancy=0
What is a venturimeter?
A tube that narrows and then widens again.
How would you find the shear force acting on a pipe from the loss in head due to friction?
If there is a nozzle with a smaller diameter than the supply, how would you find total head?
Find the velocity at the exit (use smaller diameter) and use V2/2g.
What are the processes that make up a carnot cycle?
Two isothermal and two adiabatic.
What does a pitot static tube measure?
What is the equation for the work done in an isothemal process?
w=R*T*ln(V1/V2)
How do you find the log mean temperture difference?
Find the temperture differences between the hot pipe and the cold pipe.
