A water pump can generate a pressure difference Δp (psi) given by Δp=145-0.1 Q^2, where the flow

step 1 In this equation we have to find the flow rate, the pressure drop, and the power supply of the p

A water pump can generate a pressure difference Δp (psi)...

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 in., roughness 0.5 in.. and length 2500 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?

Key Concepts

Pump Performance Curve

This concept refers to the relationship between the pressure difference (or head) a pump can generate and the flow rate it produces. It is fundamental in understanding how operating conditions change as the load increases, and it enables engineers to match the pump to the system demands.

Friction Loss in Pipe Flow

This concept involves the loss of pressure due to friction as a fluid flows through a pipe. It depends on factors such as pipe diameter, length, internal roughness, and the flow rate. Equations like the Darcy?Weisbach equation or similar correlations are used to estimate these losses, which are crucial for determining the required pump performance.

Pipe Roughness and Its Effect on Friction

Pipe roughness is a measure of the texture of the interior surface of the pipe. It significantly influences the friction factor and, hence, the head loss experienced during flow. A lower roughness value typically leads to reduced frictional losses, allowing higher flow rates or reduced energy consumption for the same flow.

Hydraulic Power and Pump Efficiency

Hydraulic power represents the useful mechanical work done by the fluid, which is computed from the pressure and flow rate. Pump efficiency accounts for the losses during the conversion of input power into hydraulic power. The actual power supplied to the pump must compensate for these inefficiencies to achieve the desired fluid transport.

Transcript

Please give Ace some feedback