Question

Starting from the results of Examples 5.4 and 5.5, estimate the number of cubic meters of water that would flow each second through an OTEC plant large enough ( 1000 M W e 1000 MWe) to provide electricity for Miami. Use the approximation of an ideal heat engine as in the examples. If this water flows at a velocity of 4 m / s 4 m/s, what would be the necessary diameter of the pipes?

Answer 1

Answer: Hello Results of examples 5.4 and 5.5 are missing from your question but I was able to find it online and use it to resolve your question

answer :

a) 1780 m^3/sec

b)  23.81 m

Explanation:

a) calculate the number of m^3 of water flowing through an OTEC plant charge

assumption : assuming an ideal heat engine

 Q / t   =  m*c*∆T * (eff) / t

1e^9 J/s = 1g/cc *V(1cal/g°C) * 2°C (6.7%)*(4.184J/cal) / t

Hence:  V / t ( number of m^3 of water ) = 1.78e^9 cc / sec = 1.78 * 10

= 1780 m^3/sec

b) Determine the diameter of pipes

Given that the water flows at  4m/s  ( velocity )

1780 m^3 /sec = A * V  ------ ( 1 )

A = π*d^2/4 =  1780 / 4 = 445 m^2  -------- ( 2 )

v = 4 m/s

Back to equation 2

d^2 = ( 445 * 4 ) / π

      ≈ 567

∴ necessary diameter ( d ) = $\sqrt{567}$ = 23.81 m