A pump is needed to lift water from a well though a height of 3.0 m at a rate of
0.6kg/min. What must be the minimum power of the pump in watts, and in horsepower?
0.6kg/min * 9.81N/kg * 3.0m * 1min/60s = ____ W
0.6*9.8*3.5=20.601/60
=0.34335W*1hp/746W
=4.6*10^4.hp
Why did the water go to therapy? Because it had a lot of pressure!
To find the minimum power of the pump, we need to use the formula:
Power (P) = Work done (W) / Time taken (t)
Work done is given by the formula:
Work (W) = Force (F) x Distance (d)
The force required to lift the water can be calculated using the formula:
Force (F) = Mass (m) x Acceleration due to gravity (g)
Given that the mass is 0.6 kg and the height is 3.0 m, we have:
Force (F) = 0.6 kg x 9.8 m/s^2 = 5.88 N
Distance (d) is given as 3.0 m, so the work done (W) is:
Work (W) = 5.88 N x 3.0 m = 17.64 J
Let's assume the time taken (t) is 1 minute:
Power (P) = 17.64 J / 60 s = 0.294 W
So, the minimum power of the pump is approximately 0.294 watts.
To convert this to horsepower, we can use the conversion factor:
1 horsepower = 745.7 watts
Therefore, the power of the pump in horsepower is approximately 0.294 W / 745.7 = 0.00039 hp.
That's one small pump for man, one giant leap for water-kind!
To find the minimum power of the pump, we need to consider the work done on the water to lift it through a height of 3.0 m. The formula for work done is:
Work = Force × Distance
In this case, the force is equal to the weight of the water being lifted, and the distance is the height through which the water is being lifted.
Given that the rate of water flow is 0.6 kg/min, we can find the weight of the water being lifted per minute using the acceleration due to gravity (g = 9.8 m/s^2):
Weight of water per minute = Mass × Acceleration due to gravity
= 0.6 kg/min × 9.8 m/s^2
= 5.88 N/min
To find the power, we need to convert the time unit to seconds:
Weight of water per second = Weight of water per minute ÷ 60
= 5.88 N/min ÷ 60
= 0.098 N/s
Now, let's calculate the power in watts:
Power (in watts) = Work ÷ Time
The work done is equal to the force multiplied by the distance:
Work = Force × Distance
= (Weight of water per second) × (Height)
= 0.098 N/s × 3.0 m
= 0.294 Nm/s
Finally, the power in watts can be calculated:
Power (in watts) = Work ÷ Time
= 0.294 Nm/s ÷ 1 s
= 0.294 W
Therefore, the minimum power of the pump required is 0.294 watts.
To convert from watts to horsepower, we can use the conversion factor:
1 horsepower = 745.7 watts
Power (in horsepower) = Power (in watts) ÷ 745.7
= 0.294 W ÷ 745.7
≈ 0.0004 horsepower
Therefore, the minimum power of the pump in horsepower is approximately 0.0004 horsepower.