Fluid Mechanics 4-6

What is fluid kinematics?

The study of how fluids flow and how to describe fluid motion.

The velocity field changes with what?

Position and Time

The velocity varies in different parts of an object.

True

A particles acceleration comes from______

how the flow changes in time, and how the particle changes in space as it moves through space.

Acceleration is the_______

derivative of the velocity.

What is a streamline?

A curve where that everywhere is tangent to the local instantaneous velocity vector.

Streamlines directly proportional to the V.

True

What happens to an object when it is stretched in one direction?

It usually shrinks in directions normal to that direction

If the flow is incompressible, what happens to the net volume of the fluid element?

Must remain constant(zero).

The volume of a compressible flow may increase or decrease as its density increases or decreases.

True

What is vorticity?

A measure of rotation of a fluid particle.

How is vorticity related to the angular velocity?

Vorticity is twice the angular velocity

What does it mean if the vorticity is non-zero?

The fluid particle thats occupying that space is ROTATING (vice-versa)

What is the value of fluid particles within the viscous boundary layer?

Non-Zero

The value of fluid particles outside of the boundary layer is___

0

With vorticity, in 2D flow the Z componet is equal to what?

Zero( so the equation reduces).

Consider steady, incompressible, two-dimensional flow through a converging duct

V=(u,v)=(u0+bx)i-(by)j

ax=∂U/∂t + u*∂u/∂x + v* ∂u/∂y -- first term is zero because the flow is steady.

ay=∂v/∂t + u*∂v/∂x + v* ∂v/∂y -- first term is zero because the flow is steady.

a vector = axi+ayj

What is the equation for the material derivative of pressure?

DP/Dt=dp/dt=∂P/∂t+(v + ∇)P

4-44: two cylinder equation

The flow is cylindrical, so the field depends on the radius so no x and y.

as you rotate nothing depends on theta and z:

Uo(r )= Ar +B/r = wr, then replace with ri and ro and set the equations equal and solve for A and B

Ar

solid body rotation

B/r

line vortex

With solid body rotation Utheta increases with

with the radius linerally. so further out the faster you move

If the fluid flows as a whole then what?

the particles just spin in a circle evenly spaced and its bulk rotation

With the line vortex the velocity does what?

Decreases with radius, so closer to the radius means. bigger velocity

With the line vortex, the fluid is irrotational where?

everywhere except where r = 0

When is the flow irrotational?

When the vorticity vector is equal to 0

51: Xa’

we’re looking for a new location and the flow is only symmetric about the x axis so disregrad Y, so set dt/dx to U and solve the equation for dt and integrate, do U sub and solve for xA’

exx(strain rate)

∂u/∂x-vice versa for y and z

What is the angular speed equation?

w=(2*pi*N)/60

What does the vorticity equal?

2*angular speed

How do we find the vorticity vector as a function of space?

We cross multiply i j k

What is a system?

A closed system

In a closed system mass is constant.

True.

What is a control volume?

A open system

Can mass cross the boundary in a open system?

Yes.

What does the RTT say?

Rate of change of B for the system is = to the rate of change of B inside the system.

When the control volume moves or changes shape what velocity do we use?

Relative velocity

Whats the equation for Vr?

Vr=V-Vcs

Lang

Position is known as a function of time and the location varies.

what is the lang format?

V(t)

Eularry

the position is fixed, the only thing thats changing with time are the individual molecules

Eularry equation?

V(x,y,x,t)

With maximum pressure we use?

Stagnation pressure: P+1/2pv² (not moving)

With Bernouli and unsteady:compressible

We integrate because it varies

Whats the equation Wmax?

M*emech

When we are dealing with headforms or heights which equation do we use?

the P/pg + v²/2g +z=H

What is caviation?

When the local pressure drops below the vapor pressure

Which equations do we use when there are multiple inlets?

Qnetin+Wshaftin=Emout(h+v²/2 +gz)- then Emin

Single outlet

Q+W=m(h2-h1+(delta V)²/2 +g(delta z))

Whenever we talk about elevation difference which bernouli equation do we use?

P+(p *V²/2)pgz

Fan problem

for W fan cancel everything and it equals m*ceo*V² 2 and no turbine and mechanical loss

How to find electric power rating of a fan

Wfan/efficincey

Volumetric flow rate is ?

v/t

Pressure diff

Wfan/volumetric flow rate

hturbine is

electric power output also use energy equation for output

Whenever it asks for force which equation do we use?

Momentum and consider external forces and if its at an angle use fx and fz

Blades problem

use linear momentum, and remeber that weight is puling down since its in the air, now use the energy equation for the power input and cross emch and wdotturbine bc its adding power not taking away