Fluid Motion

Pressure• Pressure – Force/Area

• Units – pascal (Pa)– Alternate Units – psi, in Hg, mb, atm, torr

• In fluids– Molecular collisions giving a change in

momentum.

– Direction is normal to the surface

• Pressure change perpendicular to equi-potential surface due to gravity.

A

FP

P0

P1

P2

P3

P4mg

Hydrostatic Equation

• Newton’s law in the vertical

PL PR

0 mgAPAPF TB

zgA

Vg

A

mgPPP BT

• Hydrostatic Equation

P0

P1

P2

P3

P4

mg

PT

PB

hP

P

gdzdP00

ghPP 0PaP 5

0 10013.1

z = 0

z = -h

Grand Coulee Dam

• What is the pressure at the base of Grand Coulee Dam which is 150 m deep?

• Notice the difference between absolute pressure and gauge pressure.

Archimede’s Principle

• Any body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

• A 1 kg block of balsa wood is floating in the water. What volume of the block is floating above the water?

VgB f

mg

B

(balsa = 120 kg/m3)

Continuity Equation

• For an incompressible fluid, the flow rate (kg/s) through a closed system is constant.

t1

t1

t2

t2

t

m

t

m

21

A2A1 v2v1

constantRate Flow 2211 vAvA

t

V

t

V

21

l1

l2

t

lA

t

lA

2211

Ideal Fluid• Nonviscous - No internal

friction

• Steady - Velocity at each point remains constant

• Incompressible - Density remains constant

• Irrotational - No angular momentum about a point within the fluid

A)

B)

C)

Bernoulli’s Equation

• Start with Work-Energy Theorem

• Sum of the pressure, kinetic energy/volume, and potential energy/volume is constant along a streamline.

.221 constgyvP

(P1, v1, y1) (P2, v2, y2)

22

221

212

121

1 gyvPgyvP

PEKEW consnon

VPlAA

FlFW

)(

Water Pressure• Water flows from a 20 m tall water tower to

a shower located on the 2nd floor (5 m). What is the velocity of the water leaving the shower?

20m

5m