warman ah slurry pump

A water pump lifts water from a level 10 \mathrm{m} below the g...

Concepts

work against gravity, power, mechanical horsepower, rate of work

Explanation

The minimum power required for the pump engine is the rate at which work is done to lift water against gravity. The work done in raising mass m through height h is W=m g h. The rate at which this work is done gives the power required:

P=d t d W​=d t d m​⋅g⋅h

Power calculated in SI units (watts) can be converted to horsepower (HP) using 1 HP =746 W.

Step-By-Step Solution

Step 1

Convert mass flow rate to SI units: Given rate =30 kg/min

Convert to kg/s: 1 min 30 kg​=60 s 30 kg​=0.5 kg/s

Step 2

Calculate the power required to lift the water: Given:

• g=9.8 m/s 2
• h=10 m
• d t d m​=0.5 kg/s

So, P=(0.5 kg/s)×(9.8 m/s 2)×(10 m)=0.5×98=49 W

Step 3

Convert the power to horsepower: 1 HP=746 W Power in HP=746 49​=0.0657 HP

Final Answer

The minimum horsepower the engine should have is:

0.066 HP​ (Rounded to 2 decimal places.)