Question

A water jet that leaves a nozzle at \(60 \mathrm{m} / \mathrm{s}\) at a flow rate of \(120 \mathrm{kg} / \mathrm{s}\) is to be used to generate power by striking the buckets located on the perimeter of a wheel. Determine the power generation potential of this water jet.

Short answer

Answer: The power generation potential of the water jet is (120 kg/s) × (60 m/s).

Step-by-step solution

Calculate the momentum of the water jet

To calculate the momentum, we can use the formula: momentum = mass × velocity Given that the flow rate is 120 kg/s and the velocity is 60 m/s, we will get the momentum by: momentum = (120 kg/s) × (60 m/s)

Calculate the force exerted on the buckets

As the water jet has a linear momentum, when it strikes the buckets, it will exert a force given by Newton's second law: force = momentum / time. As the flow rate (mass flow rate) is given as 120 kg/s, we have mass / time. Multiplying this by velocity will give force. force = (120 kg/s) × (60 m/s)

Calculate work done

The work done on the buckets can be calculated using the formula: work = force × distance Now, distance is the perimeter of the wheel on which the buckets are located. We are not given the distance, but it doesn't affect the process. The work done is dependent on the force and the distance.

Calculate power generation potential

Power is the amount of work done per unit time. We can calculate the power generation potential using the formula: power = work / time We already have force (from step 2) which is (120 kg/s) × (60 m/s). Dividing this by time, we get the power generation potential. Since we don't have a specific time, we can rewrite the equation with the given information: power = (120 kg/s) × (60 m/s) Therefore, the power generation potential of the water jet is (120 kg/s) × (60 m/s).