4.3 An incompressible fluid flows at a rate of 0.015 m³/s through a pipe AB with a diameter of 0.1 m. The pipe branches at B to three smaller pipes. These are: BC-diameter 0.02 m, BD-diameter 0.025 m and BE-diameter 0.05 m. If the flow rate in BC is three times the flow rate in BE, and the average velocity in BD is 4 m/s, calculate the flow rate in the three branches and determine the velocity in AB, BC, and BE.

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Water flows through a pipe AB of diameter d1= 60mm, which is in series with a pipe BC of diameter d2= 85mm in which the mean velocity V2 = 3m/s. At C the pipe forks and one branch CD is of diameter d3 such that the mean velocity V3 is 2.5 m/s. The other branch CE is of diameter d4= 40mm and conditions are such that the discharge Q2 from BC divides so that Q4= ½ Q3. Determine Q1, Q3, Q4 and d3.

Water at 25°C is pumped at 1800 gal/min from the lower to upper reservoir, as shown in Figure below (Zı = 30 ft and z2 = 180 ft). Pipe friction losses are approximated by hf = 35V/2g, where V is the average velocity in the pipe. The pump is 80% efficient. (a) Find the head loss due to friction, hẹ in ft. in horse power (b) Compute the pump head, h, in ft and the pump power needed, Ppump (hp). Given: Specific weight of water, ywater = 62.4 lb/ft'; 1 ft/s = 448.8 gal/min. Show all calculations. Z2 = 180 ft Z¡ = 30 ft D= 6 in Pump