The dirty water from a sewage is to be pumped out at 20^∘ C using a pump and a 40 -mm-diameter p

step 1 The pump inlet is 4 meters above the sewage -free surface. Now we're given D is 0 .04 meters and

The dirty water from a sewage is to be pumped out at 20^∘ C...

The dirty water from a sewage is to be pumped out at $20^{\circ} \mathrm{C}$ using a pump and a 40 -mm-diameter pipe. Determine the maximum discharge from the pump without causing cavitation. The friction factor is $f=0.028$. The (gage) vapor pressure for water at $20^{\circ} \mathrm{C}$ is $-98.7 \mathrm{kPa}$. Neglect the loss in the submerged segment of the pipe.

Key Concepts

Energy Loss in Pipe Systems

Energy loss in pipe systems stems primarily from friction and turbulence, which reduce the available energy of the fluid. These losses must be accounted for in pump system design to ensure that pressures remain above critical values such as the vapor pressure, thereby preventing cavitation and ensuring efficient operation.

Friction Factor

The friction factor is a dimensionless number that characterizes the resistance to flow in a pipe due to friction. It depends on the roughness of the pipe’s interior and the flow regime, and is crucial for accurately predicting pressure losses using the Darcy–Weisbach equation.

Cavitation

Cavitation refers to the process where vapor bubbles form in a liquid when the local pressure falls below the liquid’s vapor pressure. In pump and pipe systems, preventing cavitation is crucial because the violent collapse of these bubbles can cause damage and reduce system efficiency.

Vapor Pressure

Vapor pressure is the pressure at which a liquid starts to boil or vaporize at a given temperature. It sets a critical threshold in fluid systems; pressures falling below this value can lead to cavitation, making it a key parameter for the safe operation of pumps.

Darcy–Weisbach Equation

The Darcy–Weisbach equation is a fundamental relation in fluid mechanics used to calculate the pressure loss due to friction in a pipe. It incorporates factors such as flow velocity, pipe diameter, friction factor, and the length of the pipe, and is essential for designing systems to avoid undesired pressure drops.

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