A pressure-relief valve has a pressure setting of 140 bar. Compute the kW loss across this valve if it returns all the flow back to the tank from a 0.0016 3 m / s pump.

To compute the power loss across the pressure-relief valve, we can use the formula for hydraulic power loss, which is given by:

P=ΔP×Q

Where:

- P is the power loss (in watts, W).
- ΔP\Delta PΔP is the pressure difference across the valve (in pascals, Pa).
- QQQ is the flow rate (in cubic meters per second, m³/s).

Given:

- The pressure setting of the valve ΔP is 140 bar.
- The flow rate Q from the pump is 0.0016 m³/s.

First, we need to convert the pressure setting from bar to pascals:

Now we can plug the values into the formula:

Calculating this gives:

P=22,400 W

Since 1 kilowatt (kW) is equal to 1,000 watts (W), we convert the power loss to kilowatts:

Therefore, the power loss across the pressure-relief valve is 22.4 kW.