1. Test 1A Same material Voluntary Outside regular class

2. General energy equation Equations: Pump head: h p = [(V 2 2 – V 1 2 )/ 2g] + ( z 2 – z 1 ) + h f + ( P 2 – P 1 )/  + h t Power added to water: Ẃ p = h p  Q Where Q represents the volumetric flow rate of the water Pump efficiency  p = [(power added to water)/ (power supplied to motor)] 100

3. Homework At the maximum rate of power generation, this hydroelectric plant takes a discharge of 141 m 3 /s. The head loss through the penstock and outlet is 1.52 m. What is the power generation (MW)?

4. Mechanical power of pump Ẃ m = 2  (rad/rev) (N/60s) T N = rpm of motor 60 s converts rpm to rev/sec T is torque; ft lbf  Ẃ m to “hp” or “kW”

5. Efficiency  p = Ẃ p / Ẃ m

6. Fluid flow No-slip concept Reynolds Number (Re) Dye experiment Laminar flow Turbulent flow Dimensional analysis – dimensionless parameter

8. Head loss General energy equation Pipe friction Hagen-Poisuelle – laminar flow Darcy-Weisbach – laminar & turbulent flows f : friction factor

10. Example An oil has a SG = 0.85 and a  =6x10 -4 m 2 /s.The oil flows through a 15cm diameter pipe at 0.02 m3/s. Find the friction loss per 100m of pipe.

13. Pipe Material Absolute Roughness, e x 10 -6 feet micron (unless noted) drawn brass51.5 drawn copper51.5 commercial steel15045 wrought iron15045 asphalted cast iron400120 galvanized iron500150 cast iron850260 wood stave600 to 30000.2 to 0.9 mm concrete1000 to 10,0000.3 to 3 mm riveted steel3000 to 30,0000.9 to 9 mm

14. Example Water at 20 o C flows at a rate of 0.05m 3 /s in a 20cm asphalted cast iron pipe. What is the head loss per kilometer of pipe?

15. Example The pump of a water distribution system has a motor with a 90% efficiency. Flow through the pump is 50 L/s. Steady flow occurs through the pump with no change in flow velocity; the inlet and outlet elevations are essentially the same. Inlet and outlet absolute pressures are 100kPa and 300kPa respectively. What is the mechanical efficiency and the temperature rise of the water due to friction?

17. Homework Water is pumped at a rate of 15 m 3 /s from the reservoir through a pipe having a diameter of 1.50m. What power must be added to the water to achieve this flow?

19. Homework - Group What power must the pump supply to the system to pump oil from the lower reservoir to the upper reservoir at a rate of 0.2 m 3 /s?

21. References Images & examples Fluid Mechanics Fundamentals & Applications, 6 th Edition, Cengel & Cimbala, McGraw Hill Applied Fluid Mechanics, 6 th Edition, Mott, Prentice Hall Engineering Fluid Mechanics, 5 th Edition Crowe, & Roberson, Wiley  Which of the examples were helpful?  Why?