Question

Single pipe with turbine) Water drains from a pressurized tank through a pipe system as shown in the figure below. The head of the turbine is equal to 116 m. If entrance effects are negligible, determine the flowrate. 50 kPa e 200 m, D 0.1 m -0.0010 m Valve (K1 -5.0) 200 m Turbine 90 elbows (K 1.0) 0-L :0389 m3/s

Answer 1

Solution –

Diameter of pipe (D) = 0.1 m

Radius of pipe (R) = 0.05 m

Area of pipe (A) = π * 0.1² / 4 = 0.00785 m².

Roughness height (K) = 0.001 m

Length of pipe (L) = 200 m

Flow rate = Q

First, we are required to find the friction factor using Nikuradse Formula as shown below,

1 210g,o()+1.74 0g1o +1.74 =

Putting values in the equation, we will get

f = 0.038

Now,

The head loss will be comprising of major head loss in the pipe (H_L) and minor head loss in pipe due to sudden expansion (H_L-1) and due to pipe bend (H_L-2), (H_L-3).

(H_L) = f*l*Q² / (12.1 * D⁵) = 62809.92 * Q².

(H_L-1) = K₁*Q²/(2*A²*g) = 421.563 * Q².

(H_L-2) = (H_L-3) = K₂*Q²/(2*A²*g) = 84.313 * Q².

Total Head loss = 63400.179 * Q².

Change in elevation – total head loss = 116

200 – 63400.179 * Q² = 116

Q = 0.04277 m³/s

So, the flow rate is 0.04277 m³/s.