mud pump submersible

A water pump lifts water from a level 10 m below the ground. Water is pumped at a rate of 30 kg /minute with negligible velocity.Caculate the minimum horsepower the engine should have to do this.

Text Solution

A water pump lifts water from a level 10 m below the ground. Water is pumped at a rate of 30 kg /minute with negligible velocity.Caculate the minimum horsepower the engine should have to do this.

AI Generated Solution

The correct Answer is:

To solve the problem of calculating the minimum horsepower the engine should have to lift water from a level 10 m below the ground at a rate of 30 kg/min, we can follow these steps:

Step 1: Convert the mass flow rate from kg/min to kg/s

The mass flow rate is given as 30 kg/min. To convert this to kg/s, we divide by 60 (since there are 60 seconds in a minute). 30 kg 1 min=30 kg 60 s=0.5 kg/s

Step 2: Calculate the gravitational potential energy change per second

The potential energy (PE) gained by lifting the water can be calculated using the formula: P E=m g h Where: - m is the mass flow rate (0.5 kg/s), - g is the acceleration due to gravity (approximately 9.81 m/s 2), - h is the height (10 m). Substituting the values: P E=0.5 kg/s×9.81 m/s 2×10 m Calculating this gives: P E=0.5×9.81×10=49.05 watts

Step 3: Convert the power from watts to horsepower

1 horsepower is equivalent to 746 watts. To convert the power calculated in watts to horsepower, we use the following formula: Horsepower=Power in watts 746 Substituting the power we calculated: Horsepower=49.05 watts 746≈0.0657 horsepower

Step 4: Final Result

Thus, the minimum horsepower the engine should have is approximately: Horsepower≈0.0657 hp or 6.57×10−2 hp

Summary

The minimum horsepower required for the engine to lift water at the specified rate is approximately 6.57×10−2 hp.