Reconsider Prob. 14€“74. In order to drain the tank faster, a pump is installed near the tank exit as in Fig. P14€“75. Determine how much pump power input is necessary to establish an average water velocity of 4 m/s when the tank is full at z = 2 m. Also, assuming the discharge velocity to remain constant, estimate the time required to drain the tank. Someone suggests that it makes no difference whether the pump is located at the beginning or at the end of the pipe, and that the performance will be the same in either case, but another person argues that placing the pump near the end of the pipe may cause cavitation. The water temperature is 30°C, so the water vapor pressure is P_v= 4.246 kPa = 0.43 m-H₂O, and the system is located at sea level. Investigate if there is the possibility of cavitation and if we should be concerned about the location of the pump.

Data problem 14-74

A 3-m-diameter tank is initially filled with water 2 m above the center of a sharp-edged 10-cm-diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere through a 100-m-long pipe. The friction coefficient of the pipe is taken to be 0.015 and the effect of the kinetic energy correction factor can be neglected.

Determine 

(a) The initial velocity from the tank 

(b) The time required to empty the tank.

Transcribed Image Text:

Water tank Pump 4 m/s