fluid of mechanics project
Budget: $10 – $30 USD
Water at 15°C is to be discharged from a reservoir at a rate of 0.018 m3 using two horizontal cast iron pipes
connected in series and a pump between them. The first pipe is 20 m long and has a 6-cm diameter, while the
second pipe is 35 m long and has a diameter of d2 = 4 cm, as shown in the figure. The water level in the
reservoir is 30 m above the centerline of the pipe. The pipe entrance is sharp-edged. A gate valve (wide-open)
is incorporated to control the flow.
Assume: Kinetic energy correction factor α = 1 for both pipes, the losses associated with the connection of the
pump are negligible.
(there is a photo here)
Counting for primary and minor losses:
a) Determine the required pumping head and the minimum pumping power.
• Write a detail solution with all steps (No hand writing will be accepted. All equations should be
typed using word equation editor).
b) Write a computer code to solve a). your answers in a) and b) should be identical.
c) Using the developed computer code, study the effect of the second pipe diameter on the required
pumping head to maintain the indicated flow rate. Let the diameter d2 vary from 2 cm to 6 cm with
increments of 0.2 cm.
• Tabulate the results for: d2, Ẇ
pump, hL2, and Re. (hL2 is the total heat loss for the second pipe).
d) Plot and comment on the following figures: d2 vs Ẇ
pump, d2 vs hL2 and d2 vs Re.
e) Answer by writing detailed comments only: what if the case pipe gets rusted and its roughness
becomes ks = 0.5 mm
connected in series and a pump between them. The first pipe is 20 m long and has a 6-cm diameter, while the
second pipe is 35 m long and has a diameter of d2 = 4 cm, as shown in the figure. The water level in the
reservoir is 30 m above the centerline of the pipe. The pipe entrance is sharp-edged. A gate valve (wide-open)
is incorporated to control the flow.
Assume: Kinetic energy correction factor α = 1 for both pipes, the losses associated with the connection of the
pump are negligible.
(there is a photo here)
Counting for primary and minor losses:
a) Determine the required pumping head and the minimum pumping power.
• Write a detail solution with all steps (No hand writing will be accepted. All equations should be
typed using word equation editor).
b) Write a computer code to solve a). your answers in a) and b) should be identical.
c) Using the developed computer code, study the effect of the second pipe diameter on the required
pumping head to maintain the indicated flow rate. Let the diameter d2 vary from 2 cm to 6 cm with
increments of 0.2 cm.
• Tabulate the results for: d2, Ẇ
pump, hL2, and Re. (hL2 is the total heat loss for the second pipe).
d) Plot and comment on the following figures: d2 vs Ẇ
pump, d2 vs hL2 and d2 vs Re.
e) Answer by writing detailed comments only: what if the case pipe gets rusted and its roughness
becomes ks = 0.5 mm