Question

The solution of flow of water in a pipe network is shown in Fig. Compute: (a) The hydraulic grade line throughout the system. (b) The pressure at each node.

Solution

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In this exercise, we are asked to solve for the hydraulic grade line HH and pressure pp of each node in the given pipe network system.

The given elevation of each node are:

  • zO=100 mz_O=100\ \mathrm{m}
  • zA=10 mz_A=10\ \mathrm{m}
  • zB=20 mz_B=20\ \mathrm{m}
  • zC=5 mz_C=5\ \mathrm{m}
  • zD=0 mz_D=0\ \mathrm{m}

The given flowrates are:  

  • Q3=170 LsQ_3=170\ \mathrm{\dfrac{L}{s}}
  • Q4=50 LsQ_4=50\ \mathrm{\dfrac{L}{s}}

The given modified resistance coffiecients are:

  • Rˉ1=20 s2m5\bar R_1=20\ \mathrm{\dfrac{s^2}{m^5}}
  • Rˉ2=51 s2m5\bar R_2=51\ \mathrm{\dfrac{s^2}{m^5}}
  • Rˉ3=280 s2m5\bar R_3=280\ \mathrm{\dfrac{s^2}{m^5}}
  • Rˉ5=310 s2m5\bar R_5=310\ \mathrm{\dfrac{s^2}{m^5}}

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