Assignment:
See diagram that shows a steam-tube in which the rate of flow of mass is dm/dt. Write down an expression for dm/dt at the turbine in terms of the density of air p.
The power P generated is equal to the rate of change of kinetic energy
P = 1/2 dm/dt (u0^2-u2^2) (i)
Show that an alternative expression is given by
P = dm/dt (u0-u2)u1 (ii)
Hence show that: u2 = 2u1-u0
Substituting in (ii) and writing u1 = u0 (1-a) show that
P = 1/2pu0^3A1Cp where the power coefficient Cp = 4a(1-a)^2