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QUESTIONS Practice Water flows through a 2-inch diameter pipe at 200 lbm/min. Its temperature is 60oF. Find the velocity of water flow (fps). Practice Water from a pipe line is diverted into weigh tank for exactly 9 minutes. Tank weight increases 4765 lbf. Water temperature is 60oF. Find the flow rate (gpm). Practice Steady flow of gas through a pipe whose diameter decreases from 1.0 meter to 60cm. The gas density decreases from 2 kg/m3 to 1.6 kg/m3. The entering velocity is 25 m/s. What is exit velocity (m/s)? Example How long will it take for level to drop from h = 3m to h = 30cm? 60 cm diameter 3 cm diameter Energy equation Comparable to First Law of Thermodynamics – conservation of energy Bernoulli Equation limited by assumptions & missing terms General energy equation – expanded factors General energy equation Terms: energy per weight of flowing fluid Units: length Convention: head General energy equation Equations: Pump head: hp = [(V22 – V12)/ 2g] + ( z2 – z1) + hf + ( P2 – P1)/ hT omitted from this equation 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 Example Water flows from a large reservoir at the rate of 1.20 ft3/s through a pipe system. See Figure. Calculate the friction losses. 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)? Elevation = 610m Penstock Powerhouse Elevation = 0 Turbine Homework The pump supplies energy to the flow causing the upstream pressure in the 12 in. pipe to be 10psi. The downstream pressure in the 6 in. pipe is 30psi. The water flow rate is 3.92 cfs. What horsepower is delivered to the flow? PB PA PUMP 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 • • • References Images & examples • • Applied Fluid Mechanics, 6th Edition, Mott, Prentice Hall Engineering Fluid Mechanics, 5th Edition Crowe, & Roberson, Wiley Which of the examples were helpful? Why?