Question

A micro hydro turbine is used to generate hydroelectric power by letting liquid water from a high elevation run through the turbine to a low elevation. The turbine is under a steady state operation condition. The inlet water and outlet water are at elevations of 10 m and 2 m, respectively. The inlet and outlet diameters are 0.3 m and 0.5 m, respectively. The inlet pressure is 2.5 bar and the outlet pressure 1 bar. The inlet and outlet temperatures are the same -20°C. The mass flow rate through the turbine is 200 kg/s. Assume no heat transfer between the turbine and the surroundings. Also assume a constant specific heat. For liquid water as an incompressible substance, its specific volume is 0.001 m®/kg. Determine the power generated (kW) by the turbine. Do not use any property tables for any ungiven property values.

Answer 1

Given:

Pressure P₁=2.5 bar

P2=1 bar

d₁=0.3 m

d₂=0.5 m

Q₁=0.2 m³/s

Applying the Bernouli equation at inlet and exit

$Q_{1}=A_{1}V_{1}$

V1 = 2.83m/s

$P_{1}/\rho g+V_{1}^{2}/2g+h_{1}=P_{2}/\rho g+V_{2}^{2}/2g+h_{2}$

$25*10^{4}/\rho g+(2.83)^{2}/2g+10=10^{5}/\rho g+V_{2}^{2}/2g+2$

By solving the above equation we get

Than the flow rate will be

$Q_{2}=A_{2}V_{2}$

Than the power generated by the Turbine is given by

$P_{output}=Q_{2}*\rho *g*h_{2}$