A superheated steam runs a turbine that provides shaft work to another system. I

Question

A superheated steam runs a turbine that provides shaft work to another system. In the input velocity (V1), temperature (T1), pressure (P1), and pipe diameter (D1)' for the steam to the turbine are known. The output rate of work done (Wout), velocity (v2), temperature (T2), pressure (P2), pipe diameter (D2), and output saturated steam concentration (x) are also known, where D1 D2, and the subscripts 1, 2, f, and g correspond to inputs (in), outputs (out), fluid, and gas, respectively 1 IN as Turbine OUT What simplified expression is correct for the energy balance of the steam turbine?

Explanation / Answer

For the givne turbine

a. for energy balance

input velocity = v1, T1, P1, D1

W'o , v2, T2, P2 are also known and so is x ( quality)

input enthalapy = m'*h1 + 0.5m'*v1^2 + m'*gz1 + W'in + Q'in

ouput enthalapy = m'h2 + 0.5m'*v2^2 + m'*gz2 + W'out + Q'out

where m' is mass flow rate

W'in = 0, Q'in = 0

hence equation C) is the best answer

b. rate of heat loss = (output rate enthalapy - input rate enthalapy) = m'(xh2 - h1 + (1 - x)h2f) + 0.5m'(v2^2 - v1^2) + m'*g(z2 - z1) + W'out - (W'in + Q'in)

also

m' = -rho1*v1*pi*D1^2/4

also

H' = -m'((xh2 - h1) - (1 - x)h2f + 0.5(v2^2 - v1^2)) + W'out - (W'in + Q'in)

m' = pi*D1^2*v1/4v1

hence

option c) is the correct answer

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