power output versus velocity profile for a wind turbine is shown in the figure below. Assume the rotor diameter is 80 meters, the air density is 1.22 kg/m3, the cut-in speed is 4 m/s, the rated speed is 13 m/s and the corresponding rated (i.e., peak) power output is 1500 kW. Calculate the power coefficient when the wind turbine is operating at wind speed of 5 m/s, 10 m/s and 13 m/s.

Problem 5 A Pelton turbine has six nozzles (see the figure to the right, credit Wikipedia). Each of the nozzles has an outlet velocity of 100 m/s and an exit area of 0.05 m². If the radius of the turbine is 3 meters, and the rotational velocity is 20 rad/s, what is the power generated by the turbine?

The front and side views of a centrifugal impeller are shown in the figure below. All symbols have their usual meanings. The outer radius of the impeller is r2 = 0.4 m and the blade height at the impeller outlet b2₂ = 0.03 m. The volume flow rate of water (density = 1000 kg/m³) through the impeller is 0.2 m³/s. The outlet blade angle 8₂ = 50 degrees and the impeller rotational speed w=1600 rpm. Assume negligible losses, and the design conditions of whirl-free and shock-free entry. The impeller torque is B₂F N-m. Front View 12 b2 |+| Side View

An inflow to a turbine with a discharge of 20 m³/s leads to a ration speed of 150 rpm. The blades inlet edges have an angle of 120° to the direction of whirl. The outer diameter of the runner is 1.5 m and the runner inlet width is 1.0 m. 5. (a) To plot the velocity triangle at the blade outlet edge. (b) Assume design operating conditions and no velocity of whirl at outlet, calculate the power delivered by the runner. (c) The elevation difference between the head race and the tail race is 23 m and the head available to the turbine is 20 m, what is the hydraulic efficiency of the turbine and overall efficiency? (d) If a model of 1/10 full scale is constructed to operate under a head of 10 m, what must be its speed, power, water consumption and overall efficiency to run under the similar conditions to the prototype?

Consider two identical wind turbines with a hub height of 40 m, one located in flat agricultural land and one located above a forest. What is the relative output power for the two turbines if the wind velocity is 10 m/s at a height of 100 m in both cases? Pagricultural/Pforest = ?