Wk3 - Pipe Networks

Question 1

What are the roles of reservoirs in water distribution? (3 points)

Answer 1

• Service storage to meet fluctuating demands
• Equalise operating pressures
• Accommodate fire-fighting and emergency requirements

Question 2

What is the formula for discharge (flow rate)?

Describe each formula and their units.

Answer 2

Q = A . V

Q = flow rate (m3/s)
A = cross-sectional area of pipe (m2)
V = section velocity (m/s)

Question 3

What are the two components of head loss (H)?

Answer 3

Frictional head losses, hf
&
Local head losses, hl

Question 4

In pipe networks, which losses are considered and why?

Answer 4

Only frictional losses will be considered as local losses are much smaller.

Question 5

What is the continuity (flow rate) equation for pipes in parallel?

What is the head loss equation for pipes in parallel?

Answer 5

Q = Q1 + Q2

H = hf1 = hf2

Question 6

When should the Darcy-Weisbach equation be used in pipe networks?

Answer 6

when ‘lambda’ or ‘K’ values are used for head loss

Question 7

When should the Hazen-Williams equation be used in pipe networks?

Answer 7

When ‘C’ is used for head loss

Question 8

What is the modified continuity equation for parallel pipes?

Answer 8

Q = A1V1 + A2V2

Question 9

What is the modified frictional head loss equation for parallel pipes?

What equation is used in place of ‘hf1’ and ‘hf2’?

Answer 9

H = hf1 = hf2

The Darcy-Weisbach or Hazen-Williams equation replaces hf1 and hf2.

Question 10

What is the formula for the Darcy-Weisbach equation?

Answer 10

H = (lamda.L.V^2) / (2.g.d)

Question 11

How is velocity calculated in parallel pipe systems?

Answer 11

Enter the data into the Darcy-Weisbach equation and calculate an answer with respect to velocity squared.

Rearrange using the total head loss to solve for ‘V’.

Question 12

How do you calculate discharge in a parallel pipe system once ‘V1’ and ‘V2’ has been calculated?

Answer 12

Input the data into the modified continuity equation:

Q = A1V1 + A2V2

Question 13

What is the modified continuity equation for pipes in series?

Answer 13

Q = Q1 = Q2

Question 14

What is the modified frictional head loss equation for pipes in series?

Answer 14

H = hf1 + hf2

Question 15

What does the modified Darcy-Weisbach equation for frictional head loss become with pipes in Series?

Answer 15

H = (lamda.L.V^2/2gd)1 + (lamda.L.V^2/2gd)2

Question 16

How is the modified continuity equation rearranged to solve for V in pipes in series?

Answer 16

Q = V1A1 = V2A2

V2 = V1.(A1/A2)

Question 17

What are the stages to calculating discharge in pipes in series?

Answer 17

1. Solve using Darcy Weisbach or Hazen-Williams to get ‘H=…V1^2 + …V2^2’
2. Rearrange continuity to get ‘V2=V1.(A1/A2)
3. Substitute ‘V2’ into step 1 to solve for ‘V1’
4. Use V1 to solve for V2, Q1 and Q2

Question 18

What is the cross-sectional area of a pipe equal to?

Answer 18

Pi.D^2/4

Question 19

How do you calculate the new flow rate between reservoirs if a new pipe is laid in parallel along two pipes in series?

Answer 19

1. New flow rate, Q prime = Q3 + Q (Q= pipes 1 and 2)
2. Solve for V3 using Darcy Weisbach and ‘H’ value
3. Calculate A3, then Q3=A3V3
4. Add Q3 to Q

Question 20

In looped systems, what assumptions must be made?

Answer 20

• Net flow at any node = 0
• Flow in at node = Flow out
• Net head loss around the loop = 0

Question 21

What are the stages to the Hardy-Cross method of solving for the flows within a looped system?

Answer 21

1. Assume values of ‘Q’ in each system to satisfy continuity in each node.
2. Calculate head losses in each section of the loop.
3. Check whether the net head loss around the loop is zero, if not, apply a correction factor to the assumed values of ‘Q’ and start again from ‘step 2’.

Question 22

What is the sign convention for looped flows?

Answer 22

Clockwise flow = +ve and vice versa

Question 23

How is headloss calculated in a loop?

Answer 23

Using the expression provided in the question.

Typically: hf = K x Q^2

Question 24

How do you know when you have calculated the final flow rate volumes?

Answer 24

When the sum of frictional losses is close to or equal to ‘0’

Question 25

How do you calculate the pressure head at nodes using an initial pressure head at ‘A’?

Answer 25

Use the values of ‘hf’, final head losses, calculated previously. Don’t forget to recalculate for A.

B = A - AB
C = B - BC
A = C - AC

Question 26

What is the formula for the correction factor?

Answer 26

q = - (Sum(hf))/(2(Sum(hf/Q)))