Logistic

A pipe network as shown in Figure 1 has been constructed in order to convey water from a central supply (A) to a number of delivery points. A pump has been installed in the line between A and D in order to boost the pressure as water flows from A to D.

The details of each pipe are given in the table below, all are comprised of galvanised iron with a roughness height of k = 0.16 mm.

Pipe	AB	BC	CD	DE	EF	FA	AD
Length(m)	220	500	250	200	200	250	400
Diameter(mm)	200	150	150	100	150	200	150

The head added by the pump is a function of the flow rate and may be expressed using:

For the purpose of linearization of the pipe network it may be expressed as

where Q 7* represents the estimate of the flow in pipe 7 in the same manner as in the expression for friction loss, e.g. *

H f  r| Q 7| Q 7

(note that if you cannot understand the equation for Hp you may assume the pump is adding a constant head of 21 m, but you will not receive full marks)

Task

a) Use the linearisation method to solve for the unknown discharges in each pipe.

b) The pressure head at point A is measured at 50 m (head of water). Assuming the network is situated on a level grade estimate the pressure head in metres at each pipe junction (B, C, D, E & F)

c) What is the operating point (H & Q) of the pump?

HINT: The pump has the opposite effect (opposite direction) to the friction loss in pipe A-D