Pipe network

Question 1

Conservation of Volume

Answer 1

Qin= Qout

Question 2

Q can be assumed to be +ve if

Answer 2

• It is the highest head endpoint

- It is the lowest head endpoint

Question 3

Approximating

Answer 3

Qab1=Qab0-

fQab0)/
(f’Qab0

Question 4

Describe steps in the hardy Cross method to determine flow rates

Answer 4

1. for each arc in network, write down darcy-weisbach equation relating head difference to flow rate.
2. For each node, use conservation of volume to references to the arcs volume flow rate from equations.
3. For each closed loop in system, add darcy-weisbach equations for all arcs in the loop to produce an equation that sets a function of the flow rates equal to 0.
4. Associate each loop function with one of the remaining flow rates.
5. Obtain an expression for derivative of each loop function with respect to one of the remaining flow rates
6. Make a guess at each of the remaining flow rates
7. For each equation setting a loop function to 0, use one step of the newton- rahpson method to update only the flow rate associated with that loop function.(pretend that the function is a function of only one variable, using a single-variable newton raphson method)
8. repeat step 7 until a stable set of a flow rate values is achieved.

Awkward iterative method needed because one cannot invert an equation of the form.