Unit 3: Conservation Laws Flashcards
What is a control volume?
An arbitrary volume in space through which fluid flows
What is a control surface?
The control surface is the surface of the control volume
What is volume flow rate and mass flow rate?
Q: the volume of the fluid flowing through a cross section per unit time
ṁ: The amount of mass flowing through a cross section per unit time
In what conditions can the continuity equation be simplified?
Incompressible fluid: ρ is independent of time or spece > you can take it out of the integral > the densities cancel eachother
∫vdA = Q
Incompressible fluid + nondeformable CV:
∫vdA = Q = 0
Steady flow: ∂/∂t = 0 > the right side = 0 (Mass flow rate into CV = Mass flow rate out of CV)
∫ρvdA = 0
Uniform velocities at the cross section: replace the integral with a sum.
∫vdA = ΣvA = 0
When is the continuity equation used
When you are given most velocities and areas and need to calculate the last velocity or area.
Useally there are no forces in the problem
What are the assumptions behind Bernoulli’s equation?
Steady flow
Incompressible flow
Frictionless flow
Flow along a streamline
(Ideal fluid)
What defines steady flow?
The Mass flow rate into a fixed control volyme is equal to the Mass flow rate out of the control volume
∂/∂t = 0
What defines incompressible flow
The Volume flow rate into a fixed control volyme is equal to the Volume flow rate out of the control volume
ρ = constant
What defines frictionless flow
When there are no viscous forces acting on the fluid
μ = 0
What is a streamline
A streamline is a curve that is everywhere tangent to the
instantaneous local velocity vector
What are the terms of the bernoulli equation called?
think about head
Elevation head: z (gravitational potential energy)
Pressure head: P/γ (Flow work)
Velocity head: v^2/2g (Kinetic energy)
Piezometric head: z + P/γ (The sum of the first 2 terms above)
Total head: H (The sum of the first 3 terms above)
What’s the difference between Energy grade line and Hydraulic grade line?
EGL corresponds to the total head
HGL corresponds to the piezometric head
How can the bernoulli equation be modified to work with real fluids?
You add the head loss to the right side of the equation.
H(s) = H0 - ∆H
What does the components of the momentum equation represent?
FB = body forces
FS= surface forces
∂/∂t ∫ρvdV = rate of change of linear mumentum in the control volume (CV)
∫vρv*dA = rate at which linear mumentum is exiting the control surface (CS)
In what conditions can the Momentum equation be simplified?
Uniform flow:
∫vρvdA -> ΣρvAv
Steady flow:
∂/∂t ∫ρvdV = 0
