Flooded Basement Water is pumped steadily out of a flooded basement at a speed of 5.5 m/s through a uniform hose of radius 0.8 cm. The hose passes out through a window 3.1 m above the waterline. What is the power of the pump?

To find the power of the pump, we can use the equation:

Power = Force × Velocity.

First, we need to find the force exerted by the water coming out of the hose. By using the equation:

Force = Pressure × Area.

The pressure at a certain depth in a fluid is given by:

Pressure = density × gravity × height.

Given that the water is pumped from the basement, we can assume the density of water to be approximately 1000 kg/m³ and the acceleration due to gravity to be 9.8 m/s².

The height difference between the waterline and the window is given as 3.1 m. Therefore, the pressure exerted by the water is:

Pressure = 1000 kg/m³ × 9.8 m/s² × 3.1 m = 30,340 Pa.

Next, we need to calculate the area of the hose. The radius is given as 0.8 cm, which is 0.008 m. Hence, the area is:

Area = π × radius² = π × (0.008 m)² = 0.00020106 m².

Now that we have the pressure and the area, we can find the force exerted by the water:

Force = Pressure × Area = 30,340 Pa × 0.00020106 m² = 6.1149 N.

Finally, we can calculate the power of the pump using the force and the velocity of the water:

Power = Force × Velocity = 6.1149 N × 5.5 m/s = 33.63395 W.

Therefore, the power of the pump is approximately 33.6 Watts.

To calculate the power of the pump, we need to use the equation:

Power = (Pressure)*(Flow Rate)

First, we need to calculate the flow rate. The flow rate can be determined using the equation:

Flow Rate = (π*(Radius)^2)*(Velocity)

Given that the radius of the hose is 0.8 cm, we need to convert it to meters by dividing by 100:

Radius = 0.8 cm = 0.8/100 m = 0.008 m

The velocity of the water is given as 5.5 m/s.

Now, we can calculate the flow rate:

Flow Rate = (π*(0.008 m)^2)*(5.5 m/s)

Next, we need to calculate the pressure. Since the hose passes out through a window 3.1 m above the waterline, it will have a potential energy difference. The pressure can be determined using the equation:

Pressure = (Density)*(Gravity)*(Height)

The density of water is approximately 1000 kg/m^3 and the acceleration due to gravity is approximately 9.8 m/s^2. The height difference is given as 3.1 m.

Now, we can calculate the pressure:

Pressure = (1000 kg/m^3)*(9.8 m/s^2)*(3.1 m)

Finally, we can calculate the power of the pump:

Power = (Pressure)*(Flow Rate)

Substitute the values we calculated for pressure and flow rate to find the power.