Question

A vertical draft tube is installed on a Francis Turbine and the total head to the center of the spiral casing at the inlet is 38 meters and velocity of water at the inlet is 5 m/s. The discharge is 2.1 cubic meters/second. The hydraulic efficiency is 0.87 and overall efficiency is 0.84. The velocities at the inlet and exit of the draft tube are 5 m/s and 1.5 m/s respectively. The top of the draft tube is 1 m below the center line of the spiral casing while the tailrace (water) level is 3 meters from the top of the draft tube. There is no velocity of whirl at either top or bottom of the draft tube and leakage losses are negligible. What is the power output of the turbine in kw? [20%]

A. 987.8
B. 901.3
C. 746.9
D. 832.6
E. 632.9

Answer 1

The power output of a Francis Turbine is computed by calculating the hydraulic power using the effective head and flow rate and then adjusting for the turbine's overall efficiency. The effective head accounts for the kinetic energy changes at the draft tube's inlet and outlet.The correct option is option c .

Step-by-step explanation:

The question asks for the power output in kW of a Francis Turbine given the total head, inlet velocity, discharge, and efficiencies. To calculate the power output, we need to use the formulas for hydraulic power with respect to the head and flow rate, and then apply the efficiency factors. The hydraulic power (P) provided by the head of water can be calculated as P=ρ g Q H, where ρ is the density of water (1000 kg/m3), g is the acceleration due to gravity (9.81 m/s2), Q is the discharge (flow rate), and H is the effective head.

The effective head takes into account the differences in kinetic energy between the inlet and the outlet of the draft tube, calculated using Bernoulli's principle. As the velocities at the inlet and exit of the draft tube are given, we can use the formula H = Hstatic + (v12 - v22)/(2g) where v1 and v2 are the velocities at the inlet and exit of the draft tube, respectively.

To find the actual power output of the turbine, we apply the overall efficiency (ηoverall) to the hydraulic power. Thus, the power output Poutput = ηoverall • P. Plugging in the given values, we calculate the power output and find the answer that aligns with the options provided in the question.