urbines convert the energy of the fluid into mechanical energy. Turbines are often used in power plants with generators to produce electricity. One such installation is shown in Fig. 2.19. A dam is constructed to store water and to produce required head. Water passes through the turbine and goes

Question

Turbines convert the energy of the fluid into mechanical energy. Turbines are often used in power plants with generators to produce electricity.
One such installation is shown in Fig. 2.19. A dam is constructed to store water and to produce required head. Water passes through the turbine and goes downstream. Determine power available to the turbine when the flow rate is [latex]30 {m^{3}}/{s}[/latex].

Accepted Answer

Area of exit pipe [latex]a_{2} = \frac{\pi}{4} D^{2}_{2} = \frac{\pi}{4} imes 2.7^{2} = 5.72 m^{2}[/latex]

From equation of continuity [latex]Q = a_{2} V_{2}[/latex]

[latex] herefore V_{2}={Q}/{a_{2}}= {30}/{5.72}= 5.2 {m}/{s}[/latex]

Applying Bernoullis equation in modified form at points 1 and 2

[latex] \frac{P_{1}}{\gamma }+ \frac{V^{2}_{1}}{2g}+Z_{1}= \frac{P_{2}}{\gamma }+\frac{V^{2}_{2}}{2g}+Z_{2}+H_{T}[/latex]

where

[latex]H_{T}[/latex] = represents head developed by turbine

[latex]P_{1} = P_{2}[/latex] = atmospheric pressure = 0

[latex]V_{1} = 0[/latex] because of large reservoir.

Substituing proper values,

[latex] 0 + 0 + 20 = 0 + \frac{5.2^{2}}{2 imes 9.8} + 6 + H_{T}[/latex]

[latex] herefore H_{T} = 12.6 m[/latex]

Power developed by the turbine in K W

[latex] P=\gamma QH_{T} = 9800 imes 30 imes 12.6 = 3704400 w[/latex]

[latex] P=3704 kw[/latex]

Question 2.6: urbines convert the energy of the fluid into mechanical ener...

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