A popular brand of pressure washer claims to deliver 330 litres per hour of water at a pressure of 80 bar, drawing 1400 W of electrical power in the process. Pressure washers of this type consist of an electric motor that drives a small compressor to pressurize water fed into it through a garden hose.

Show that the amount of power in the water flow when the washer is in operation is approximately 736 W
Calculate the efficiency with which the electrical input energy is converted to hydraulic energy in the water
Calculate the diameter of the output nozzle of the washer
Assuming all the pressure is dropped at the output nozzle, use its cross-sectional area to calculate the reaction force exerted on the user when the washer is in operation

how can I get to the answers for this

question

To calculate the amount of power in the water flow, we can use the formula:

Power = Flow rate * Pressure

Given that the flow rate is 330 liters per hour and the pressure is 80 bar, we need to convert these values to a consistent unit system. Let's convert the flow rate to liters per second and the pressure to Pascals:

Flow rate = 330 liters/hour = 330/3600 liters/second ≈ 0.092 liters/second
Pressure = 80 bar = 80 * 10^5 Pascals

Now we can calculate the power:

Power = 0.092 liters/second * 80 * 10^5 Pascals
= 7.36 * 10^3 liters * Pascals / second
≈ 7.36 * 10^3 W

Therefore, the amount of power in the water flow is approximately 736 W.

To calculate the efficiency with which the electrical input energy is converted to hydraulic energy, we can use the formula:

Efficiency = (Power output / Power input) * 100%

The power output in this case is the calculated power in the water flow, which is 736 W. The power input is given as 1400 W.

Efficiency = (736 W / 1400 W) * 100%
≈ 52.57%

Therefore, the efficiency with which the electrical input energy is converted to hydraulic energy in the water is approximately 52.57%.

To calculate the diameter of the output nozzle of the washer, we can use the formula:

Flow rate = (π/4) * (diameter^2) * velocity

Given that the flow rate is 0.092 liters/second, and assuming a constant velocity, we can rearrange the formula to solve for the diameter:

diameter = √((4 * Flow rate) / (π * velocity))

However, the velocity of the water coming out of the nozzle is not given in the problem statement. We need this information to calculate the diameter accurately.

To calculate the reaction force exerted on the user when the washer is in operation, we can use the principle of conservation of momentum. Assuming all the pressure is dropped at the output nozzle, we can equate the change in momentum of the water to the reaction force on the user.

Change in momentum = mass of water * change in velocity

The mass of water can be calculated using its density and volume:

mass of water = density of water * volume of water

Given that the density of water is approximately 1000 kg/m^3, and the volume of water flow is 330 liters/hour, we convert it to cubic meters per second:

volume of water = 0.092 liters/second = 0.092 * 10^(-3) cubic meters/second

Now we can calculate the mass of water:

mass of water = 1000 kg/m^3 * 0.092 * 10^(-3) cubic meters/second

Next, we need to determine the change in velocity. This can be calculated using Bernoulli's equation, which states the conservation of energy in a fluid flow system. The equation is as follows:

(Pressure + (1/2) * density * velocity^2) = constant

Since all the pressure is dropped at the output nozzle, the equation becomes:

(1/2) * density * inlet velocity^2 = (1/2) * density * outlet velocity^2

Since the density is common on both sides, we can cancel it out:

inlet velocity^2 = outlet velocity^2

Therefore, the change in velocity is given by:

change in velocity = inlet velocity - outlet velocity = inlet velocity

We don't have the inlet velocity information in the problem statement, so we cannot calculate the change in velocity accurately.

As a result, we cannot calculate the diameter of the output nozzle or the reaction force exerted on the user without the necessary additional information.