How much work is done by a pump with a 0.1m diameter piston, travelling 250mm against a pressure of 1500kPa?

To determine the work done by the pump, we can use the formula for work involving a piston, which is:

[

\text{Work} = \text{Pressure} \times \text{Area} \times \text{Distance}

]

First, we need to find the area of the piston, which is circular. The area ( A ) can be calculated using the formula:

[

A = \pi \left( \frac{d}{2} \right)^2

]

where ( d ) is the diameter of the piston. Here, the diameter is 0.1 m, so the radius ( r ) is 0.1 m / 2 = 0.05 m. Therefore, the area becomes:

[

A = \pi (0.05)^2 \approx \pi (0.0025) \approx 0.007854 , \text{m}^2

]

Next, we convert the distance traveled by the piston into meters. Since it travels 250 mm, this is equivalent to 0.25 m.

Now, substituting the values into the work equation where the pressure ( P ) is given in kPa