Hydroelectric plant turbine selection.
Based on the provided data, we can use the following steps to determine the type of turbines, specific speed, and size of the turbines, as well as the location of the centerline of the turbine with respect to the water level and check for cavitation using Thoma's criteria.
Step 1: Determine the flow rate
The flow rate can be calculated using the formula:
Q = P / (ρgh)
where Q is the flow rate, P is the installed capacity (60 MW), ρ is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and h is the net head (20 m).
Plugging in the values, we get:
Q = 60,000,000 / (1000 x 9.81 x 20) = 306.1 m³/s
Step 2: Determine the specific speed
The specific speed (Ns) can be calculated using the formula:
Ns = (n √Q) / (H)^(3/4)
where n is the rotational speed (in revolutions per minute), Q is the flow rate (in cubic meters per second), and H is the net head (in meters).
Plugging in the values, we get:
Ns = (750 x √306.1) / (20)^(3/4) = 64.5
Step 3: Determine the type of turbine
Based on the specific speed, we can determine the type of turbine using the following classification:
Francis turbine: Ns = 10 to 100
Propeller turbine: Ns = 100 to 1,000
Kaplan turbine: Ns = 1,000 to 10,000
Pelton turbine: Ns = 10,000 to 100,000
Since the specific speed falls in the range of 10 to 100, a Francis turbine is suitable for this application.
Step 4: Determine the size of the turbine
The size of the turbine can be determined based on the flow rate and the specific speed. The Francis turbine can be designed to have an efficiency of around 90%, based on the provided draft tube efficiency. Therefore, the power output can be calculated as:
Pout = η x Pin
where Pout is the power output, η is the efficiency (0.9), and Pin is the power input (60 MW).
Plugging in the values, we get:
Pout = 0.9 x 60,000,000 = 54,000,000 W
The power output can also be calculated as:
Pout = ρQgHη
where ρ is the density of water (1000 kg/m³), Q is the flow rate (306.1 m³/s), g is the acceleration due to gravity (9.81 m/s²), H is the net head (20 m), and η is the efficiency (0.9).
Plugging in the values, we get:
Pout = 1000 x 306.1 x 9.81 x 20 x 0.9 = 54,000,000 W
The size of each turbine can be calculated as follows:
Pout = ωT x (π/30) x D^2 x L x ρ/4
where ωT is the angular velocity of the turbine, D is the diameter of the turbine, L is the length of the turbine, and ρ is the density of water.
We can assume a specific speed of 65 for the Francis turbine and use empirical equations to determine the diameter and length of the turbine. For a specific speed of 65, the diameter and length
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