Bernoulli Equation Pitot tube o o o Horizontal

Bernoulli Equation – Pitot tube o o o 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 o • • • Fluids in motion Pumps Fans Compressors Turbines Heat exchangers

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

Flowing fluid o o 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 o (ρVA)1= (ρVA)2

Energy balance o o Kinetic Potential Flow Energy – changes in properties

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

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

Bernoulli Equation o • • • Assumptions Steady state Incompressible fluid No friction in fluid stream

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

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

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

Example o During a trip, motorist runs out of fuel. A helpful driver allows you to siphon fuel from her auto. (2) is located 0. 75 m below (1); (3) is 2 m above (1). Siphon diameter is 4 mm. Find the minimum time to transfer 4 L of fuel & the pressure at (3). Fuel density is 750 kg/m 3.

Homework o 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 o 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 o Steady flow of gas through a pipe whose diameter decreases from 1. 0 meter to 60 cm. 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 o. Images & examples • • Mechanics of Fluids, 3 rd 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 Mc. Graw Hill q. Which of the examples were helpful?