A water pump can generate a pressure difference \(\Delta p\) (psi) given by \(\Delta p=145-0.1 Q^{2}\), where the flow rate is \(Q \mathrm{ft}^{3} / \mathrm{s}\). It supplies a pipe of diameter \(20 \mathrm{in}\)., roughness \(0.5 \mathrm{in}\). , and length \(2500 \mathrm{ft}\). Find the flow rate, pressure difference, and the power supplied to the pump if it is 70 percent efficient. If the pipe were replaced with one of roughness 0.25 in., how much would the flow increase, and what would the required power be?