A syphon of diameter 200 mm connects two reservoirs having a diff
| A syphon of diameter 200 mm connects two reservoirs having a difference in elevation of 20m. The length of syphon is 500 m and the 3.0 m above the water level in the upper reservoir. The length of the syphon from upper reservoir to the summit is 100 m. Find out the discharge through syphon. Neglect minor lessees. The coefficient of friction, f = 0.005.
A. 87.9 m<sup>3 </sup>/ sec
B. 87.9 liters/sec
C. 87.9 cm<sup>3</sup> / sec
D. 87.9 mm<sup>3</sup> / sec
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Right Answer is: B
SOLUTION
Applying Bernoulli’s equation between point A & B
\(\frac{{PA}}{{\rho g}} + \frac{{V_A^2}}{{2g}} + {Z_A}\)
\(= \frac{{\rho _B^2}}{{\rho g}} + \frac{{V_B^2}}{{2g}} + {Z_B} + \)(Loss of head due to friction from A to B)
⇒ O + O + ZA = O + O + ZB + hf
\(\Rightarrow {Z_A} - {Z_B} = {h_f} = \frac{{4fL{V^2}}}{{d \times zg}}\)
\(\Rightarrow 20 = \frac{{4 \times 0.005 \times 500 \times {V^2}}}{{0.2 \times 2 \times 9.81}}\)
⇒ V = 2.8 m/s
\(\therefore Q = \frac{\pi }{4}{d^2}v = \frac{\pi }{4} \times 0.2 \times 2.8\)
⇒ Q = 0.0879 m3/sec = 87.9 liters/sec
