CEE 341 Fluid Mechanics for Civil Engineers Homework # 6 Problem 1 In a lab experiment, it has been found that the velocity profile in a pipe where the flow is turbulent (this will be defined in the next module) is: V = Vmax ¥ (1-2)", where Vmax is the maximum velocity in the centerline of the pipe; r is the radial distance from the pipe centroid; ro is the radius; and n is an exponent that depends on the flow condition and that varies between 1/6 to 1/8. Derive a formula for the kinetic energy correction coefficient a for the given velocity profile. What is a if n = 1/6? Problem 2 A pipe is attached to a tank and discharges water in the atmosphere as shown in the figure. The head losses up to point B are 0.4 m, the head losses up to the nozzle are 1 m, and the kinetic energy correction factor a is 1 everywhere. (1) What is the discharge? (2) What is the value of pressure at B? 1.5 m Water B + 40 cm diameter 3.5 m 1 «20 cm-diameter nozzle 1 Problem 3 A pipe with a venturi meter withdraws water from a tank as shown in the figure. Find the head losses at the throat of the venturi meter under these conditions: - Cavitation is just about to occur at the throat of the venturi meter. The vapor pressure of water at 20 °℃ is 2340 Pa abs. - Velocity in the portion of the pipe with diameter D is 4 m/s. D = 30 cm, d = 15 cm, Patm = 100 kPa, H = 5 m. - Assume steady flow and a = 1.0 everywhere. H D 1 Water T=20°C 0 Problem 4 A pump draws water from a tank (point A in the figure) through a pipe with diameter D = 20 cm, and discharges it into air at point C. Find the height h from the water surface to C (see figure) when: - Velocity in C is 3 m/s; - The pump receives 42 kW from the electric grid and operates at 63% efficiency; - The head loss in the pipe between A and C is 1.5 * V2/g; - a = 1 at all locations. C h Pump A Y Water 2 d