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Isfahan University of Technology (IUT) Department of Civil Engineering FLUID MECHANICS 1385-1386 Term II Assignment #4 Motion of fluid particles, part II Due: 27/1/1386 __________________________________________________________________ 1 2 3* A Pelton wheel turbine is illustrated in the figure. The radius to the line of action of the tangential reaction on each vane is 1 ft. Each vane deflects fluid by an angle of 135 as indicated. Assume that all of the flow occurs in a horizontal plane. Each of the four jets shown strikes a vane with a velocity of 100 ft/s and a stream diameter of 1 in. The magnitude of velocity of the jet remains constant along the vane surface. How much torque is required to hold the wheel stationary? A 2-ft-diameter cylindrical drum of water, lying on its side, is being emptied through a 2-in-diameter hole at the bottom of the drum. The velocity of the water out of the hole is 2gh , where h is the height of the water surface above the outlet of the tank. Initially the tank is half-full. Find the time for the tank to empty. 135 1 ft 1 in. Vent 2 ft 2 in. h 4 ft V A pump transfers water from one reservoir to another as shown in the figure. The friction head loss in the pipe is given by KLV2/2g, where V is the average fluid velocity in the pipe and KL is the loss coefficient. The relation between the pump head (hP) and the flowrate through the pump is given in the figure. If KL = 20, and the pipe diameter is 4 in., what is the flowrate through the pump? hP (m) 300 200 100 ft 100 Pump 0 0 4 1 Q (ft 3/s) 2 3 If the flow of Prob. #2 is assumed to be quasi-steady, find a relationship between the water depth, h, and time, t. 1 Assignment #4 Motion of fluid particles, part II Due: 25/1/1386 __________________________________________________________________ 5 For the system shown in the figure, find the maximum power that can be extracted from the turbine in terms of , D, and h (neglect all losses). h D T 6* An inviscid liquid drains from a large tank through a square duct of width b as shown in the figure. The velocity of the fluid at the outlet is not precisely uniform because of the h difference in elevation across the outlet. If b<<h, this difference in velocity is negligible. x For given b and h, determine v as a function of v= v(x) b b/2 x and integrate the results to determine the average velocity, V. Plot the velocity distribution, v = v(x), across the outlet if h = 1 m and b = 0.1, 0.2, 0.4, 0.6, 0.8, and 1 m. How small must b be if the difference between the centerline velocity, v at x = b/2, and the average velocity is less than within 3% of the average velocity? 7* Salt water flows from tank A through a hole with diameter d = 100 mm, as indicated in the figure. Initially (time = 0) tank A contains concentrated salt water with a specific gravity of 1.15 and tank B contains pure water. Each tank has a diameter of 2 m and initial liquid depth of 3 m. Prove that the specific gravity of the liquid in tank B as a function of time can be expressed as, SG 6.45 1.15 1.732 0.221t 6 1.732 0.221t 2 A 2m d 2 Neglect viscous effects and assume that the liquid in tank B is mixed continuously so that the specific gravity is uniform throughout the tank. Also assume that the flow is quasi-steady (Bernoulli equation can be used). How long does it take for tank A to be emptied? 2 B 2m