The diagram shows a tank draining into another lower tank through a pipe. Note the velocity and pressure is both zero on the surface on a large tank. Calculate the flow rate using the data given on the diagram. (Ans. 7.16 dm3/s)

The diagram shows a tank draining into another lower tank through a pipe. Note the velocity and pressure is both zero on the surface on a large tank. Calculate the flow rate using the data given on the diagram. (Ans. 7.16 dm3/s)

Solution

 h1 + z1 + u1 2 /2g

 = h2 + z2 + u2 2 /2g 0 + z1 + 0 = 0 + 0 + 0 + hL

 hL = 20 

20 = 4 Cf Lu2 /(2 g d) + minor losses

 20 = {4 x 0.007 x 50u2 /(2 x 9.81 x 0.05)} + 0.5 u2 /(2 x 9.81) + u2 /(2 x 9.81) = 29.5 u2 /(2 x 9.81) 

u = 20(2 x 9.81)/ 29.5 = 3.65 m/s 

A = 0.00196 m2 Q = Au =0.00196 x 3.65 = 0.00716 m3 /s or 7.16 dm3/s