It is suggested to connect the Mediterranean Sea with the Dead Sea with a closed tunnel and use the potential difference in levels to produce electric energy. What is the diameter required to generate the power specified?

The data of the proposed system are (here the Mediterranean sea is the dam and the Dead sea is the discharge point while the tunnel is the penstock)

:

• Elevation Difference = 401 m (it probably increased 10 more meters in the past 40 years).
• Distance between the seas (Channel length) is: 50 miles= 80,467 m
• Power produced = 600 MW (use consistent units of W)
• Turbine efficiency 90%
• Friction factor  f =8*g*(e/D)²*(4/D)^{2.6*(e/D)^0.5}
• Tunnel is made of concrete with Relative roughness = 0.012
• From economic considerations the velocity should be: >= 2 m/s  (this is recommended for the Hydroelectric power stations. You can use up to 10 m/sec.

You should end up with a nonlinear algebraic equation in D and solve it numerically  

high reservoir dam turbine penstock (c) high head