Bernoulli Equation – Pitot tube  Horizontal  Velocity at stagnation point is 0  Incompressible fluid  Steady state  Velocity as function of pressure difference

Hot Wire Anemometer

One Minute Paper Statics

Fluid dynamics  Fluids in motion Pumps Fans Compressors Turbines Heat exchangers

Conservation  Energy & mass; neither created nor destroyed in ordinary process  Control volume  Steady state: no accumulation nor depletion

Flowing fluid  Steady flow  Uniform flow  Mass flow rate: Kg/ time, lbm/time  Volume flow rate: m 3 /time, ft 3 /time, cfm, gpm

Continuity Mass flow rate Volume flow rate

Nozzle  (ρVA) 1 = (ρVA) 2

Energy balance  Kinetic  Potential  Flow   Energy – changes in properties

Bernoulli Equation  Energy per weight of flowing fluid  Head Pressure Velocity Elevation

Bernoulli Equation  P/ - static pressure  V 2 /2g – velocity pressure  P T = P S + P V  V = [(2g/) (P T – Ps)] 1/2

Bernoulli Equation  Assumptions Steady state Incompressible fluid No friction in fluid stream

Bernoulli Equation  Useful because: Process flow reasonable steady Compressibility effects small Friction effects minor

Example  Water flowing from hose attached to a main at 400kPa. Boy covers most of hose outlet with thumb, producing a vertical, thin jet of high speed water. What is maximum height of jet?

Example  A large tank open to the atmosphere is filled with water. A tap near the bottom of the tank is opened to allow flow from a smooth, rounded opening. Find the outlet velocity.

Example  During a trip, motorist runs out of fuel. A helpful driver allows you to siphon fuel from her auto. (2) is located 0.75m below (1); (3) is 2m above (1). Siphon diameter is 4mm. Find the minimum time to transfer 4 L of fuel & the pressure at (3). Fuel density is 750 kg/m 3.

Homework  Water flows through a 2-inch diameter pipe at 200 lbm/min. Its temperature is 60 o F. Find the velocity of water flow.

Homework  Water from a pipe line is diverted into weigh tank for exactly 9 minutes. Tank weight increases 4765 lbf. Water temperature is 60 o F.

Homework  Steady flow of gas through a pipe whose diameter decreases from 1.0 meter to 60cm. The gas density decreases from 2 kg/m 3 to 1.6 kg/m 3. The entering velocity is 25 m/s. What is exit velocity?

References  Images & examples Mechanics of Fluids, 3rd Edition, Potter & Wiggert, Brooks & Cole Applied Fluid Mechanics, 6 th Edition, Mott, Prentice Hall Engineering Fluid Mechanics, 5 th Edition Crowe, & Roberson, Wiley Fluid Mechanics Cengel & Cimbala McGraw Hill  Which of the examples were helpful?