Pipe Network

Q. The Chezy's coefficient C is related to Darcy-Weisbach friction factor 'f' as

1. $C=\sqrt{\left(\frac{g}{8f}\right)}$
2. $C=\sqrt{\left(\frac{8g}{f^{\frac{1}{4}}}\right)}$
3. $C=\sqrt{\left(\frac{8g}{f}\right)}$
4. $C=\sqrt{\left(\frac{f}{8g}\right)}$

Q.

A pipe of 0.7 m diameter has a length of 6 km and connects two reservoirs A and B. The water level in reservoir A is at an elevation 30 m above the water level in reservoir B. Halfway along the pipe line, there is a branch through which water can be supplied to a third reservoir C. The friction factor of the pipe is 0.024. the quantity of water discharged into reservoir C is 0.15 m${}^3$/s. Considering the acceleration due to gravity as 9.81 m/s${}^2$ and neglecting minor losses, the discharge (in m${}^3$/s) into the reservoir B is

1. 0.572

Q. Which one of the following conditions must NOT be satisfied in the Hardy-Cross analysis of pipe network?

1. Continuity principle demands that flow into a network junction is equal to the flow out of it.
2. Momentum equation must be satisfied so that the force in each loop is balanced.
3. Darcy-Weisbach head loss equation is to be used in computing head loss in elementary circuits. The equation is of the form $h_L=K{Q}^n.$
4. $\sum h_L=\sum k{Q}^n$ must be equated to zero. If not, a flow correction factor $△$Q is to be made for arriving at a solution.
   

Q.
A pipe network consists of a pipe of 60 cm diameter and branches out at a point T into two branches, one of 30 cm diameter and the other of 45 cm diameter. These branch pipes rejoin at a point B. The velocity in the first branch (of 45 cm diameter) is 1.5 m/sec. Which one of the following statements is true?

1. The velocity in the second branch is 1.0 m/sec.
2. The velocity in the second branch is 2.25 m/sec.
3. The velocity in the second branch is $\frac{2}{3}=0.667m/sec$.
4. The potential drop between T and B in both branches is the same.

Q. In a pipe network :

1. The algebraic sum of discharges around each elementary circuit must be zero
2. The head at each node must be the same
3. The algebraic sum of the drop in piezometric head around each elementary circuit is zero
4. The piezometric head loss in each line of each circuit is the same

Q.

A triangular pipe network is shown in the figure



The head loss in each pipe is given by $h_f=r.Q^{1.8}$ with the variables expressed in a consistent set of units. The value of r for the pipe AB is 1 and for the pipe BC is 2. If the discharge supplied at the point A (i.e., 100) is equally divided between the pipes AB and AC, the value of r (up to 2 decimal places) for the pipe AC should be

1. 0.62

Q. The circular water pipes shown in the sketch are flowing full. The velocity of flow (in m/s) in the branch pipe "R" is

1. 3
2. 4
3. 5
4. 6

Q. A channel of width 450 mm branches into two sub-channels having width 300 mm and 200 mm as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is $0.9m^3/s$ and the velocity in the sub-channel of width 200 mm is 3 m/s, the velocity in the sub-channel of width 300 mm is_______m/s. Assume both inlet and outlet to be at the same elevation.

1. 1

Q. Three reservoirs A, B and C are interconnected by pipes as shown in the figure. Water surface elevations in the reservoirs and the Piezometric head at the junction f are indicated in the figure.


Discharges Q${}_1$, Q${}_2$ and Q${}_3$ 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. Consider the following conditions for the pipe network shown in the given figure (Notations have the usual meaning with suffixes 1, 2 and 3 referring to respective pipes):

1. $Q_1=Q_3$
2. $Q_2=Q_1+Q_3$
3. $h_{f1}=h_{f3}$
4. $h_{f1}=h_{f2}=h_{f3}$

Which of these conditions must be satisfied by this pipe network?

1. 1 and 3
2. 2 and 3
3. 1 and 4
4. 2 and 4

Q. A pipe of 324 mm diameter, having friction coefficient as 0.04, connects two reservoirs with 15 m difference in their water levels through a 1500 m long pipe. What will be the discharge through the pipe?

1. 104 lps
2. 134 lps
3. 165 lps
4. 196 lps

Q. The procedure to be followed in solving for discharge in a simple pipe problem, when $h_f,L,D,V\text{and}\epsilon \text{are given is to}$
[Note: Re is Reynolds number,
f = friction coefficient,
$\frac{\epsilon }{D}=\text{relative roughness}$
V = velocity]

1. assume f, compute: V, Re, $\frac{\epsilon }{D}$ and calculate f; and repeat if necessary
2. assume Re, compute f, check $\frac{\epsilon }{D}$
3. assume V, compute Re and calculate f, V again
4. assume $\epsilon \text{compute V, Re, and calculate f}$