Water at 20 °C is pumped through a 2 cm inner diameter commercial steel pipe at

Question

Water at 20 °C is pumped through a 2 cm inner diameter commercial steel pipe at a flow rate of 25 L/min (400 gal/hr). The pipe section is horizontal and has 1 globe valve (2 cm id). The pressure at the entry point of the pipe is 700 kPa (gauge). A small leak develops 122 m (400 ft) downstream of the entry point. a) Compute the fluid pressure at the point of the leak. Solve this problem in the S.I. system and report your answer in kPa of the leak is 0.254 cm and a discharge coefficient of 0.61 steel pipe (internal diameter 1.049 in) and an entry pressure of 103 psig and leak diameter of units ofka min. Assume the diameter c) Solve this problem (parts a and b) in English/Imperial Units for 1-in schedule 40 commercial 0.10 in. Report your answers in psi and Ibm/min.

Explanation / Answer

a) Reynold Number, Re = Density*velocity*pipe diameter/ viscosity of water

velocity,v=flowrate(Cross sectional area of pipe)

=>v=25*10^-3/60/(3.14/4*.02^2)=1.32 m/s

viscosity of water=8.9*10^-4 Pas

=>Re=1000*1.32*.02/(8.9*10^-4)=29663

Roughness of steel pipe = .1 mm

=>Relative roughness = roughness/pipe diameter = .1/20=.005

From moody's chart, Friction factor, f =..045

equivalent length in globe valve for friction loss = k/f*Pipe diameter

For Globe valve, k=10

=>equilvalent length corresponding to globe valve = 10/.045*.02=4.44 m

=> Downstream total length,l = 4.44+122 =126.44 m

Pressure drop = f*(.5*density*v^2*l)/Pipe diameter = .045*(.5*1000*1.32^2*126.44)/.02=247847 Pa = 247 Kpa

=> Pressure at downstream at leakage point = Inlet pressure - Pressure drop = 700-247=453 Kpa

flowrate through leak = Discharge coefficient*(2*deltaP/density)^.5*leakage area

P outside leakage = 1 atm = 100 Kpa

delta P = (453-100)=353 kpa

=>flowrate thorugh leakage = .61*(2*353000/1000)^.5*(3.14/4*.254^2*10^-4)=8.2*10^-5 m3/s

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.