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Task 2
Scenario: The water in a large lake is to be used to generate electricity by installing a
hydraulic turbine-generator at a location where the depth of water is 50 m. Water is to be
supplied at a rate of 5000 kg/s. If the electric power generated is measured to be 1960 kW.
Determine the generator efficiency.
V
Lake
h = 50 m
Turbine
Generator
m = 5000 kg/s
Figure 2a A turbine generator diagram
laminar region
y transition
turbulent
8
U.
U.
U...
U.
viscous sublayer
X=0
surface of plate
Figure 2b
Task 2.1 (p2.1)
Referring to Figure 2a, determine the electric power generated by the generator. Use
conservation of mechanical energy = [mass * (e mech_in- e mech_out) ], at the
turbine/generator infrastructure to find the amount of energy involved.
Task 2.2 (p2.2)
The Bernoulli's equation is given as follows:
4 (119)
3
ipuż + pgz2 + p2 = žpu; + pgzı + pi
where
p represents pressure, p refers to density, and gequals to gravitational force, z
refers to elevation.
Explain on how the Bernoulli equation can be applied in moving fluid where the equilibrium of
energy is maintained.
Task 2.3 (p2.3)
Discuss on the limitations on the use of the Bernoulli equation. Give example on where the
Bernoulli's equation is applicable in terms of volume and mass transfer rate.
Task 2.4 (p2.4)
Consider the flow of a fluid over a flat plate as shown in Figure Q2b. Discuss the boundary
layer region which involves the heat transfer and velocity change on the fluid. The incurred
drag force involves with the friction coefficient. Explain the other factors which could affect
this drag force calculation and how they are applied in the turbulent flow?
Task 2.5 (p2.5)
The pressure loss in a tube or duct can be expressed by the D'Arcy-Weisbach equation.
Assuming the flow in a pipe is steady and incompressible, determine the factors which could
affect the frictional heat losses (pressure loss) in the pipe as explained by the
D'Arcy-Weisbach equation.
Use an example on pressure loss in a pipe to demonstrate how the energy loss can be
calculated.
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Task 2.0
Generator efficiency is given
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 𝑂𝑢𝑡𝑝𝑢𝑡
𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 𝐼𝑛𝑝𝑢𝑡
The generator efficiency is assumed to be 0.95
Task 2.1
𝑃
Mechanical power input = 𝜌 = 𝑔ℎ
Mechanical power input = (9.81m/s2 × 50m)/1000kJ/kg = 0.491kJ/Kg
But the rate at which the water is supplied is 5000Kg/s.
Therefore, mechanical power input = 0.491kJ/kg × 5000Kg/s = 2455Kj/s = 2455kW.
Turbine Generator efficiency = 1862kW/2455kW = 0.758 = 0.76 or 76%
Turbine-generator efficiency = Turbine efficiency ×generator efficiency
Turb...
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