Piping Network: Sometimes it is desirable to analyze a piping network. Depending on the data given, an approach can be formulated. Consider the following case:

Case 1: The pressure and elevations information at points 1, 2, 3, and 4 are provided. Pipe diameters, lengths and roughness information for pipes A, B, and C are also provided. It is desired to find quantities of fluid flowing through these pipes.

One can make use of the equation where frictional head loss is provided and find the Reynolds number. This procedure can also be applied to remaining three pipes. Check to ensure that mass is conserved i.e.

Example 4.16: A piping network is given below. Find out flow rates through pipes #1, #2, and #3. Pipe #1 (AB) is a horizontal pipe at an elevation of 50 feet. Other end of pipe #2 (BC, point C) has an elevation of 10 feet. Other end of pipe #3 (BD, point D) has an elevation of - 10 feet. Both pipes #2 and #3 have equal pressure drop of 3.7 psi (533 psf). Use the following information:

Roughness of the pipe = 0.00015 ft

Density = 62.37 lb/ft³

Viscosity = 7.53 ´ 10^-4 lb/(ft·s)

Pipe	Segment	L/ft	d/ft	RR
1	AB	200	0.1723	0.0087
2	BC	100	0.1342	0.0011
3	BD	100	0.0848	0.0018

Solution: Applying Bernoulli equation between points B and C, frictional loss in pipe #2 can be found to be

Now we can find the value of the group ReÖf by using d₂, and L₂ as

Figure 4.4 can be used to find friction factor as 0.005. This value of friction factor corresponds to Reynolds number of 1.54 ´ 10⁵ (Figure 4.3). Once Reynolds number is known we can find the velocity of the fluid through the pipe #2.

We can do a similar analysis for pipe #3. We can calculate h_f3 to be 68.54 ft·lb_f/lb. Then the group ReÖf for pipe #3 is found to be 7.112 ´ 10³. Figure 4.4 can be used to find friction factor to be 0.006. This value of friction factor corresponds to Reynolds number of 9.08 ´ 10⁴. The velocity of the fluid through pipe #3 can be calculated as 12.54 ft/s. Now knowing the velocities in the pipes #2 and #3 we can calculate the combined flow rate by multiplying velocities in the individual pipes by their cross-sectional areas. This can also result in the velocity of the fluid in pipe #3.

And the combined flow rate is

The Reynolds number can be calculated to be 1.66 ´ 10⁵. Friction factor can be obtained from Figure 4.3 as 0.005. And the frictional losses can be computed to be

Pressure drop in pipe #1 is, therefore,

However, if the pressure is given at point A, C, and D and volumetric flow rates through pipes are required, then pressure at point B is found such that mass is conserved and pressure drop for the estimated flow rates matches with the given pressure. This may involve some iteration.