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Tutorial on Internal flows

1. Determine the loss of head in friction when water at 15 deg C flows through a 300

mm long galvanised pipe of 150 mm diameter at 0.05 m3/s. Kinematic viscosity of

water at 15 deg C is 1.14 10-6 m2/s. Average surface roughness is 0.15 mm.

Calculate the pumping power required to maintain the above flow.

2. Oil of kinematic viscosity 10-5m2/s flows at a steady rate through a cast iron pipe of

100 mm diameter and of 0.25 mm average surface roughness. If the loss of head over

a pipe length of 120 m is 5 m of the oil, what is the flow rate through the pipe.

3. Determine the size of a galvanised iron pipe needed to transmit water a distance of

180 m at 0.085 m3/s with a loss of head of 9 m. Water of kinematic viscosity 1.14

10-6m2/s is considered. The surface roughness is 0.15 mm.

4. Air at a temperature of and standard pressure flows from a furnace through an 200

mm diameter pipe with an average velocity of 3. m/s. It then passes through a

transition section and into a square duct whose side is of length a. The pipe and ductsurfaces are smooth. Determine the duct size, a, if the head loss per meter is to be the

same for the pipe and the duct

5. Crude oil flows through a level section of the Alaskan pipeline at a rate of 2.944 m 3/s.

The pipe inside diameter is 1.22 m; its roughness is 0.1524 mm. The maximum

allowable pressure is 8.27 Mpa; the minimum pressure required to keep dissolved

gases in solution in the crude oil is 344.5 kPa. The crude oil has specific gravity of

0.93; its viscosity at the pumping temperature of 60C is 0.0168 Pa.s. For these

conditions, determine the maximum possible spacing between pumping stations. If

the pump efficiency is 85%, determine the power that must be supplied at eachpumping station.

6.

Water flows (density = 1000 kg/m3and viscosity of 1.307 10-3Pa.s) from a large

reservoir to a smaller one through a 5 cm diameter cast iron piping system.

Determine the elevation z1for the flow rate of 6 litres/second. Roughness is 0.00026

m

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7. A bathroom plumbing of a building consists of 1.5 cm diameter copper pipes with

threaded connectors. (a) if the gage pressure at the inlet of the system is 200 kPa

during a shower and the toilet reservoir is full (no flow in that branch), determine the

flow rate of water thorugh the shower head. Take the loss coefficients of the shower

head and the reservoir to be 12 and 14 respectively. = 1000 kg/m3= 0.001 Pa.s

8.

Three pipes with diameter, length and friction factor values of (D1, L1, f1); (D2,L2,f2); and (D3, L3, f3) are connected in parallel between two points A and B in a

pipeline. If an equivalent pipe (De, Le, fe) is to replace the set of parallel pipes, obtain

an expression for estimating the equivalent pipe diameters.

9.

A compound piping system consists of 1800 m of 50 cm, 1200m of 40 cm and 600 m

of 30 cm diameter pipes of the same material connected in series. Assume that the

friction factors in each pipe is same

a. What is the equivalent length of 40 cm pipe of the same material

b. What is the equivalent size of a pipe 3600 m long

c.

If the three pipes are in parallel, what is the equivalent length of a 50 cm pipe

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