Find the work required to pump the water out of the spout.

Question

A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s² for g. Use 1000 kg/m³ as the density of water. Assume r = 3 m and h = 1 m.)

Answer 1

To find the work required to pump the water out of the spout, you can calculate the potential energy of the water in the tank and then convert it into work. The potential energy of an object is given by the formula:

Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)

Given:

- Water density (ρ) = 1000 kg/m³

- Inner radius of the tank (r) = 3 m

- Height of the water column (h) = 1 m

- Acceleration due to gravity (g) = 9.8 m/s²

First, let's calculate the volume of water in the tank. To do this, we'll find the volume of the cylinder formed by the water.

Volume of water = π * r² * h

Volume of water = π * (3 m)² * 1 m

Now, calculate the mass of the water by multiplying the volume by the water density:

Mass of water (m) = Volume of water * Water density

Mass of water = [π * (3 m)² * 1 m] * 1000 kg/m³

Now, calculate the potential energy (work done) required to pump the water out of the spout:

Potential Energy (PE) = Mass of water * Gravitational acceleration * Height

Potential Energy = [π * (3 m)² * 1 m] * 1000 kg/m³ * 9.8 m/s² * 1 m

Calculate this expression to find the potential energy in joules. This represents the work required to pump the water out of the spout. If you want the result in a different unit, such as joules or kilojoules, you can convert it accordingly.