A pump is needed to drain an excavation at a construction site. The excavation has a length of 50m, width of 50m, and a depth of 4m. The surface of the water in the excavation lies at a depth, H=3m, from the top the of the excavation. An old, radial flow, 1000W pump is immediately available for use; however, the total pump-motor efficiency, e, is only 50%. Estimate the drawdown in the excavation in the first 4 hours of pumping. Neglect the change in H with increasing time. Neglect any head loss in the hose/pipe connected to the pump. (Hint: utilize the Pout equation, consider an alternative definition of discharge as a change in volume over a change in time). Assume a specific weight of 9.79kN/m 3 .

Question

A pump is needed to drain an excavation at a construction site. The excavation has a
length of 50m, width of 50m, and a depth of 4m. The surface of the water in the excavation lies at a
depth, H=3m, from the top the of the excavation. An old, radial flow, 1000W pump is immediately
available for use; however, the total pump-motor efficiency, e, is only 50%. Estimate the drawdown in
the excavation in the first 4 hours of pumping. Neglect the change in H with increasing time. Neglect
any head loss in the hose/pipe connected to the pump. (Hint: utilize the Pout equation, consider an
alternative definition of discharge as a change in volume over a change in time). Assume a specific
weight of 9.79kN/m 3 .