Negative Work Cases: Pipes and Cisterns Basics A negative work case refers to a situation where the actual output is less than the desired output. Let's expl...
A negative work case refers to a situation where the actual output is less than the desired output. Let's explore how this applies to pipes and cisterns and how to calculate the negative work case for each.
Pipes:
Imagine a pipe with water flowing through it. The pipe has a diameter of 10 cm and the flow rate is 0.5 L/s. If the pipe's length is 100 cm, the flow will be laminar and the pressure will decrease along the pipe.
If the pressure at the entrance of the pipe is 1 atm and the pressure at the end of the pipe is 0.5 atm, the negative work case will occur. This means that despite the flow rate being higher than the desired flow rate, the pressure is lower at the end of the pipe than it is at the entrance.
Cisterns:
A cistern is a container with a hole at the bottom. Water flows into the container through the hole at a constant flow rate. If the diameter of the hole is smaller than the diameter of the container, water will not flow into the container. This is because the pressure inside the container is higher than the pressure outside the container.
If the diameter of the hole is 10 cm and the diameter of the container is 20 cm, the negative work case will occur. This means that despite the flow rate being constant, the pressure inside the container is higher than the pressure outside the container. Therefore, the water will not flow into the container.
Calculating the Negative Work Case:
To calculate the negative work case for a pipe or a cistern, we can use the formula:
Negative Work = Pressure at entrance - Pressure at exit
Negative Work = Initial pressure - Final pressure
Remember:
A negative work case always occurs when the actual output is less than the desired output.
The negative work case can be calculated for both pipes and cisterns.
A higher flow rate leads to a lower pressure at the end of a pipe or a higher pressure inside a container