A tank of water empties by gravity through a siphon into a lower tank. The difference in levels is 6 m and the highest point of the siphon is 2 m above the top surface level. The length of pipe from the inlet to the highest point is 3 m. The pipe has a bore of 30 mm and length 11 m. The friction coefficient for the pipe is 0.006.The inlet loss coefficient K is 0.6.

 A tank of water empties by gravity through a siphon into a lower tank. The difference in levels is 6 m and the highest point of the siphon is 2 m above the top surface level. The length of pipe from the inlet to the highest point is 3 m. The pipe has a bore of 30 mm and length 11 m. The friction coefficient for the pipe is 0.006.The inlet loss coefficient K is 0.6.

 Calculate the volume flow rate and the pressure at the highest point in the pipe. 

Solution

Total length = 11 m Cf = 0.006 

Bernoulli between (1) and (3) 

h1 + u1 2 /2g + z1 = h3 + u3 2 /2g + z3 + hL 

0 + 6 + 0 = 0 + 0 + 0 + hL                        hL= 6

 hL= Inlet + Exit + pipe 

6 = 0.6 u2 /2g + u2 /2g + (4 x 0.006 x 11/0.03) u2 /2g 

6 = 0.6 u2 /2g + u2 /2g + 8.8 u2 /2g = 10.4 u2 /2g 

u = 3.364 m/s 

Q = A u = (π x 0.032 /4) x 3.364                     Q = 0.002378 m3 /s 

Bernoulli between (1) and (2) 

h1 + u1 2 /2g + z1 = h2 + u2 2 /2g + z2 + hL

 0 + 0 + 0 = h2 + 2 + u2 /2g + hL

 hL= Inlet + pipe = 0.6 u2 /2g + (3/11) x 8.8 u2 /2g 

hL= 0.6 x 3.3642 /2g + (3/11) x 8.8x 3.364/2g 

hL= 1.73 m

 0 = h2 + 2 + 3.3642 /2g  + 1.73

 h2 = -4.31 m