Flow through Branched Pipes

Q. Two long pipes in parallel are used to carry water between two reservoirs. The diameter of one pipe is twice that of the other. Both the pipes have the same value of friction factor. Neglect minor losses. What is the ratio of flow rates through the two pipes?

1. 2.8
2. 5.6
3. 8
4. 11.3

Q. Three reservoirs A, B and C are interconnected by pipes as shown in the given figure. Water surface elevations in the reservoirs and the piezometric level at the junction D are also indicated in the figure.

$\text{Flow}{Q}_1,Q_2\text{and}{Q}_3\text{are related as}$

1. $Q_1+Q_2=Q_3$
2. $Q_1+Q_2=Q_3$
3. $Q_2-Q_1=Q_3$
4. $Q_1+Q_2+Q_3=0$

Q. Two reservoirs are connected by two pipes P and Q. The pipes have the same diameter and length and are placed in parallel. If the friction factor of P is 9 times that of Q, then the discharge in P to that in Q is

1. 0.5
2. 0.45
3. 0.33
4. 0.27

Q. Water flows into junction J from reservoirs A and B through connecting pipes, the head loss through these being, respectively $10.Q_A^{2}and4.Q_B^2$. The water level elevations at the reservoirs at A and B are 25.9 m and 18 m, respectively. The inflow at J is discharged out at C into the atmosphere. The head loss through pipe JC is $1.Q_C^2$. The gauge pressure at J is 9 m. What is the residual gauge pressure of the outflow at C?

1. 2.56 m
2. 1.86 m
3. 1.16 m
4. 0.46 m

Q. Three pipes A, B and C have the following basic geometries :

Pipe	A	B	C
Diameter	D	D/2	2D
Length	L	L	4L

If these pipes are connected in series, by assuming the value of friction factor f to be same for all the three pipes and the equivalent pipe, this set of pipes in series is equivalent pipe, of length $L_e$ and diameter D and friction factor f with the equivalent length $L_e$ being equal to

1. $5\frac{1}{8}L$
2. $4\frac{1}{8}L$
3. $26\frac{1}{8}L$
4. $33\frac{1}{8}L$

Q.

On dropping a stone in stationary water circular ripples are observed. The rate of flow of ripples is$6cm{s}^{-1}$. When the radius of the circle is$10cm$, then the fluid rate of increase in its area is

1. $120c{m}^2{s}^{-1}$

2. $12c{m}^2{s}^{-1}$

3. $\pi c{m}^2{s}^{-1}$

4. $120\pi c{m}^2{s}^{-1}$

Q. Two tanks A and B, of constant cross-sectional area of $10m^{2}and2.5m^2$, respectively, are connected by a 5 cm pipe, 100 m long, with f = 0.03. If the initial difference of water levels is 3 m, how long will it take for $2.5m^3$ of water to flow from A to B? Considering entry and exit losses, it can be grossly assumed that the flow velocity, it can be grossly assumed that the flow velocity, in m/s, through the pipe is $1.75\sqrt{h}$, where h is in m, taking g = 10 m/sec${}^2$, also, may take area of pipe as $2\times {10}^{-3}{m}^2$.

1. 535 seconds
2. 516 seconds
3. 485 seconds
4. 467 seconds

Q. Two reservoir maintain a constant difference of water levels of 11.25 m and are connected by a 10 cm diameter pipeline of 294.3 m length. The total of all head losses, by friction valve losses, bend losses, inlet and exit losses, and velocity head can be taken as $98.1v^2/2g$ (in m) where v is the flow velocity through the pipe (in m/sec). Assuming that the valve at the downstream end is suddenly opened so that there is no pressure wave, what will be the time taken for the velocity of flow in the pipe to attain 95% of the steady terminal velocity? Take
$\frac{1}{9.81}=0.102$.

1. $2.25lo{g}_{e}19$
2. $2lo{g}_{e}19$
3. $2.25lo{g}_{e}39$
4. $2lo{g}_{e}39$