a water pump takes 20 minutes to pump water to fill a tank of volume 40 metre if the efficiency of pump is 40% and the tank is at the height 15 how electric power is needed for a pump
Answers
Explanation:
Here, Volume of water =30 m
3
t=15 min=15×60 s=900 s;Height,h=40 m
Efficiency, η=30%
Density of water =10
3
kg m
−3
∴ Mass of water pumped =Volume×Density
=(30 m
3
)(10
3
kg m
−3
)=3×10
4
kg
P
output
=
t
W
=
t
mgh
=
900 s
(3×10
4
kg)(10 ms
−2
)(40 m)
=
3
4
×10
4
W
Efficiency, η=
P
input
P
output
P
input
=
η
P
output
=
3×
100
30
4×10
4
=
9
4
×10
5
=44.4×10
3
W=44.4 kW.
Given
- Volume of tank = 40 m³
- Density of Water = 10³ kg/m³
To Find
- Electric Power needed
Solution
● Mass = Volume × Density
● Work Done = Potential Energy = mgh
● Power = Work/Time
● Ep = 30% of power needed
✭ Mass of the water pumped :
→ Mass = Volume × Density
→ Mass = 40 × 10³
→ Mass = 4 × 10⁴ kg
✭ Work Done :
→ Work = mgh
→ Work = 4 × 10⁴ × 9.8 × 40
→ Work = 1568 × 10⁴ J
→ Work = 1.568 × 10⁷ J
✭ Power Required :
→ Power = Work/Time
- Work = 1.568 × 10⁷ J
- Time = 20 min = 20 × 60 = 1200 sec
→ Power = (1.568 × 10⁷)/1200
→ Power = 13.006 kW
✭ Electric Power Consumed :
→ Electric Power = 30% of power needed to pump
→ Electric Power = 13.066 × 30/100
→ Electric Power = 3.9 kW