A pump is used to lift 500 kg of water from a depth of 80 m in 10 seconds.Calculate the power rating of the pump if it's efficiency is 40% . Take g=10 m/ s*s.
To calculate the power rating of the pump, we need to first calculate the work done by the pump, and then divide it by the time taken.
Step 1: Calculate the work done by the pump
The work done (W) is given by the formula:
W = m * g * h
Where:
m = mass of water lifted = 500 kg
g = acceleration due to gravity = 10 m/s^2
h = height lifted = 80 m
Plugging in the values, we get:
W = 500 kg * 10 m/s^2 * 80 m
W = 400,000 J (Joules)
Step 2: Calculate the actual work done by the pump
Since the efficiency of the pump is given as 40%, the actual work done (W_actual) by the pump is:
W_actual = efficiency * W
W_actual = 0.4 * 400,000 J
W_actual = 160,000 J
Step 3: Calculate the power rating of the pump
The power (P) is given by the formula:
P = W_actual / t
Where:
t = time taken = 10 seconds
Plugging in the values, we get:
P = 160,000 J / 10 s
P = 16,000 W (Watts)
Therefore, the power rating of the pump is 16,000 Watts.
To calculate the power rating of the pump, we first need to find the work done by the pump in lifting the water, and then divide it by the time taken.
Step 1: Calculate the work done by the pump.
Work is given by the formula: work = force × distance
Given:
Mass of water (m) = 500 kg
Height (h) = 80 m
Acceleration due to gravity (g) = 10 m/s^2
The force required to lift the water is the weight of the water, which is given by the formula: force = mass × acceleration due to gravity
force = m × g = 500 kg × 10 m/s^2 = 5000 N
Now, let's calculate the work done:
work = force × distance = 5000 N × 80 m = 400,000 J (Joules)
Step 2: Calculate the power.
Power is given by the formula: power = work / time
Given:
Time (t) = 10 seconds
power = 400,000 J / 10 s = 40,000 W (Watts)
Step 3: Calculate the power rating with efficiency.
The efficiency of the pump is given as 40%. Efficiency is defined as the ratio of output power to input power.
Let's denote the power rating of the pump as PR.
efficiency = (output power / input power) × 100
Using the given efficiency, we can calculate the input power:
efficiency = 40%
input power = 100% = 40% / efficiency = 100% / 40% = 2.5
output power = input power × efficiency = 2.5 × 40,000 W = 100,000 W
The power rating of the pump is 100,000 W or 100 kW.
F = M*G = 500 * 10 = 5000 N.
P = F*d/(t*0.4) = 5000*80/(10*0.4) = 100,000 Watts.