Fluids my cards

Q=

AV for same density

V1=

Q/A1 (if you find Q you can use that to find V1)

m=

pQ

Momentum equation for Steady flow

Fx= Accumlation term

Accumlation integral simplifies to

p2A2V2- p1A1V1

Conservation of Energy Prob

cancel out internal energy if not given, Cancel out pressure if both are atm, cancel out gravity if horizontal, cancel out Q if no heat transfer

How is stream function derived for unique shape

superposition of simpler shapes such as uniform + doublet

When says 2a upstream

add the radius then the 2a

Angle for stream function

the upstream and downstream so horizontal is 180 up and 0 down if left to right

Velocity r in terms of stream

1/r partial derivative with respect to theta

Velocity theta in terms of stream

-partial derivative with respect to r

Velocity for equation after derivatives

use magnitude

If a cylinder was rotating how would it affect

would create lift on top if rotating clockwise and the bottom pressure distrubution would be uneven where theres more streamlines on the top and less on the bottom

How is stream function in respect to velocity potential

it is orthogonal (\[ u=\frac{\partial\psi}{\partial y}, \])

Irrotation Flow

Partial with respect to and x- partial with respect to u and y = 0 ( woudl equal a constant if spinning.)

V rel with moving control surfave

Vrel= V- Vref

F surf

pressure due to pipe bending or wall exerting on air

F surf equation

P1A1-P2A2 (add costheta or sin theta for each if bends)

Flux integral simplifies to

mu2-mu1 (u= x velocity component so if diagonal use Vcos(30)

if trying to find P1

could use atms bernoulli where p1=-1/2pv1²(if you know v1)

for energy equation

use pressure and velocities of inlet and outlet for the equation

Stream Uniform

Stream source/sink

stream vortex

stream doublet

stream cylinder

internal streamlines

wake

pocket with no streamlines directly after an object due to viscous effects

realistic flow for viscous effects

conservation of mass compressible flow

conservation of mass incompressible flow

Differential convservation of mass for

infinitesimally tiny fluid element at a point

use differential cons of mass for

velocity field where x y and w take partial of that with respect to each

when asked to solve for streamlines

use points given and sub into function then set equal to and solve for y

for steady flow simplification remember

F= muout-muin (can have multiple outlets or inlets)