Test 1A Same material Voluntary Outside regular class.

Test 1A

Same material Voluntary Outside regular class

General energy equation

Equations: Pump head: hp = [(V2

2 – V12)/ 2g] + ( z2 – z1) + hf +

( P2 – P1)/ + ht

Power added to water: Ẃp = hp Q

Where Q represents the volumetric flow rate of the water

Pump efficiency p = [(power added to water)/ (power supplied to motor)] 100

Homework

At the maximum rate of power generation, this hydroelectric plant takes a discharge of 141 m3/s. The head loss through the penstock and outlet is 1.52 m. What is the power generation (MW)?

Mechanical power of pump

Ẃm = 2 (rad/rev) (N/60s) T

• N = rpm of motor• 60 s converts rpm to rev/sec• T is torque; ft lbf Ẃm to “hp” or “kW”

Efficiency

p= Ẃp/ Ẃm

Fluid flow

No-slip concept Reynolds Number (Re)• Dye experiment• Laminar flow• Turbulent flow• Dimensional analysis – dimensionless

parameter

Head loss

General energy equation• Pipe friction• Hagen-Poisuelle – laminar flow• Darcy-Weisbach – laminar & turbulent

flows• f : friction factor

Example

An oil has a SG = 0.85 and a =6x10-4 m2/s.The oil flows through a 15cm diameter pipe at 0.02 m3/s.

Find the friction loss per 100m of pipe.

Pipe Material

Absolute Roughness, e

x 10-6 feetmicron

(unless noted)

drawn brass 5 1.5

drawn copper 5 1.5

commercial steel 150 45

wrought iron 150 45

asphalted cast iron 400 120

galvanized iron 500 150

cast iron 850 260

wood stave 600 to 3000 0.2 to 0.9 mm

concrete 1000 to 10,000 0.3 to 3 mm

riveted steel 3000 to 30,000 0.9 to 9 mm

Example

Water at 20oC flows at a rate of 0.05m3/s in a 20cm asphalted cast iron pipe. What is the head loss per kilometer of pipe?

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?

Homework

Water is pumped at a rate of 15 m3/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?

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 m3/s?

References

Images & examples• Fluid Mechanics Fundamentals & Applications, 6th Edition, Cengel &

Cimbala, McGraw Hill• Applied Fluid Mechanics, 6th Edition, Mott, Prentice Hall• Engineering Fluid Mechanics, 5th Edition Crowe, & Roberson, Wiley

Which of the examples were helpful?

Why?