Flow through Parallel Pipes

Q. Three parallel pipes connected at the two ends have flow-rates $Q_1,Q_{2}and{Q}_3$ respectively and the corresponding frictional head losses are $h_{L1},h_{L2},and{h}_{L3}$ respectively. The correct expressions for total flow rate (Q) and frictional head loss across the two ends $\left(h_L\right)$ are

1. $Q=Q_1+Q_2+Q_3;h_L=h_{L1}+h_{L2}+h_{L3}$
2. $Q=Q_1+Q_2+Q_3;h_L=h_{L1}=h_{L2}=h_{L3}$
3. $Q=Q_1=Q_2=Q_3;h_L=h_{L1}+h_{L2}+h_{L3}$
4. $Q=Q_1=Q_2=Q_3;h_L=h_{L1}=h_{L2}=h_{L3}$

Q. Tow tanks are connected in parallel by two pipes A and B of identical friction factors and lengths. If the size of pipe A is double than that of pipe B, then their discharges will be in the ratio of

1. 2
2. 4
3. 5.66
4. 32

Q.

A pipeline (diameter 0.3 m, length 3 km) carries water from point P to point R (see figure). The piezometric heads at P and R are to be maintained at 100 m and 80 m, respectively. To increase the discharge, a second pipe is added in parallel to the existing pipe from Q to R. The length of the additional pipe is also 2 km. Assume the friction factor, f = 0.04 for all pipes and ignore minor losses.


If there is no restriction on the diameter of the additional pipe, what would be the maximum increase in discharge theoretically possible from this arrangement?

1. 0%
2. 50%
3. 67%
4. 73%

Q. A single pipe of length 1500 m and diameter 60 cm connects two reservoirs having a difference of 20 m in their water levels. The pipe is to be replaced by two pipes of the same length and equal diameter 'd' to convey 25% more discharge under the same head loss. If the friction factor is assumed to be the same for all the pipes, the value of 'd' is approximately equal to which of the following options?

1. 37.5 cm
2. 40.0 cm
3. 45.0 cm
4. 50.0 cm

Q. An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters $d_1$ and $d_2$ (where $d_1$ = $4d_2$) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is

1. 2

Q. A pipeline (diameter 0.3 m, length 3 km) carries water from point P to point R (see figure). The piezometric heads at P and R are to be maintained at 100 m and 80 m, respectively. To increase the discharge, a second pipe is added in parallel to the existing pipe from Q to R. The length of the additional pipe is also 2 km. Assume the friction factor, f = 0.04 for all pipes and ignore minor losses.


What is the increase in discharge if the additional pipe has same diameter (0.3 m)?

1. 0%
2. 33%
3. 41%
4. 67%

Q. In a pipe network of municipal water supply, a parallel pipe is sometimes installed over a portion of the pipe mainly for

1. reducing water hammer pressure
2. decreasing the pumping power need
3. increasing the head available at the node
4. increasing the discharge

Q. Two identical pumps, each capable of delivering 0.2 cumec, against a head of 30 m, are connected in parallel. The resulting discharge is

1. 0.4 cumec against a head of 30 m
2. 0.4 cumec against a head of 60 m
3. 0.2 cumec against a head of 30 m
4. 0.2 cumec against a head of 60 m