Question 36
Water flows from a lake into a turbine that is a vertical
distance of 90 m below the lake, as shown.
The mass flow rate of the water is 2400 kg min-1.
The turbine has an efficiency of 75%.
What is the output power of the turbine?
A 26
kW B
35 kW C
1.6 MW D
2.1 MW
Reference: Past Exam Paper – June 2017 Paper 11 Q19
Solution:
Answer: A.
Power = energy / time
Water in the lake (at top)
has gravitational potential energy.
Power = GPE / time
Power = mgh / t = (m/t) gh
The mass flow rate of the
water is 2400 kg min-1. This represents the quantity (m/t).
m/t = 2400 kg min-1
To be used in the above
formula for the power of water, it should be converted into SI units.
2400 kg min-1
means that 2400 kg of water flows in 1 min.
1 min - - > 2400 kg
60 s - - > 2400 kg
1 s - - > 2400/60 = 40
kg
The mass flow rate is 40
kg s-1.
Power of water = (m/t) gh
= 40 × 9.8 × 90 = 35 280 W
This is the power available
from the water. But the turbine has an efficiency of only 75%.
Power output of turbine =
(75/100) × 35 280 = 26 460 = 26 kW
For question 36, may I know why do we use 9.8 instead of 9.81 for acceleration of free fall?
ReplyDeletethis is the value given in the list of constants
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