Fluids- The Force Momentum Equation and Bernoulli Flashcards
What is force in terms of momentum?
The rate of change of momentum (aka momentum flux)
Equation for force acting on a fluid to change momentum
F=m•(V2-V1)
Where m• is mass flowrate
What contributes to the force acting on a fluid to change its momentum?
Pressure force (cashed by pressure difference) and reaction force provided by the walls
General momentum flux equation
F=m•(β1V2-β2V1)
Where β is the correction factor for if the flow is not uniform
β given for each outlet
β=1 for uniform flow
General equation relating momentum flux and types of forces to change momentum of a fluid
m•(V2-V1)=P1A1-P2A2+Fw
Remember sign conventions
Fw is wall force
What do you have to do when momentum changes in two dimensions?
Do the calculation for the x direction and the y direction separately then do Pythagoras and trigonometry to find resultant force and angle it acts. Also treat pressure as going in same direction as velocity so might have to times by sin and cos.
When a fluid flows through a smaller area than before, what happens to its velocity and pressure?
Velocity increases
Pressure decreases
What is overall conservation of energy equation?
Q-W=ΔKe+ΔPE+ΔH
How is the main conservation of energy equation different for fluid systems?
Factorise out mass. Express change in enthalpy as internal energy and pv (pressure energy). Not interested in internal energy so remove u and Q. Use density rather than v. Get:
-W=m(1/2ΔC^2 + gΔz + Δp/ρ)
W and m are rates so have dot on top
When does Bernoulli’s equation apply?
When no work is done on a flowing fluid. For inviscid fluid (no shear and Δu = 0). Steady flow. Incompressible flow (why ρ is constant). 1D uniform flow (along single streamline).
What is the main Bernoulli equation?
0=1/2(C2^2-C1^2) +g(z2-z1)+(p2-p1)/ρ
Where C is velocity
Three different ways of expressing Bernoulli equation
p/ρ+C^2/2+gz=constant
p+1/2ρC^2+ρgz=constant
p/ρg+C^2/2g+z=constant
What is Bernoulli’s equation for gases?
p+(1/2)ρC^2=constant
Because change in potential energy is relatively small
Static pressure + dynamic pressure = constant
Cavitation
A phenomenon where the local velocity is so high that the pressure drops sufficiently for the fluid to vaporise.
How to modify Bernoulli’s equation if energy loss through friction is significant
Multiply through by ρ and add a Ploss term on the opps side to 0.
