Fluid Motion

Pressure Pressure – Force/Area Units – pascal (Pa) In fluids 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. P0 P1 P2 P3 P4 mg

Hydrostatic Equation Newton’s law in the vertical Hydrostatic Equation z = 0 P0 PT P1 P2 z = -h PL PR Hydrostatic Equation P3 mg P4 PB

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? B mg (balsa = 120 kg/m3)‏

Continuity Equation For an incompressible fluid, the flow rate (kg/s) through a closed system is constant. Dl2 Dl1 A1 A2 v2 v1 t1 t2 t1 t2

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. (P2, v2, y2)‏ (P1, v1, y1)‏

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