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193 Department of Mechanical Engineering

The document contains several numerical problems involving fluid flow concepts: 1) A pipeline with varying diameter carries water from elevation 100m to 107m. The pressure and flow rate at one end is given, and the question asks to calculate the pressure at the other end. 2) Water flows in a pipe with varying diameter and elevation. The pressure, velocity and diameter is given at one section, and the question asks to calculate the pressure at a downstream section. 3) An oil pipeline tapers and slopes downwards. The pressure and flow rate is given at the higher end, and the questions asks to calculate the velocities at both ends and the pressure at the lower end. 4) A differential

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MARSDEN RONNY
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410 views6 pages

193 Department of Mechanical Engineering

The document contains several numerical problems involving fluid flow concepts: 1) A pipeline with varying diameter carries water from elevation 100m to 107m. The pressure and flow rate at one end is given, and the question asks to calculate the pressure at the other end. 2) Water flows in a pipe with varying diameter and elevation. The pressure, velocity and diameter is given at one section, and the question asks to calculate the pressure at a downstream section. 3) An oil pipeline tapers and slopes downwards. The pressure and flow rate is given at the higher end, and the questions asks to calculate the velocities at both ends and the pressure at the lower end. 4) A differential

Uploaded by

MARSDEN RONNY
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Numericals

• A pipeline (Fig. 6.5) is 15 cm in diameter and it is at an elevation of 100 m at section A. At section B it is at an elevation of 107 m and has
diameter of 30 cm. When a discharge of 50 litre/sec of water is passed through this pipeline, pressure at A is 35 kPa. The energy loss in pipe
is 2m of water. Calculate pressure at B if flow is from A to B.
• Solution
• DA = 15 cm = 0.15 m; DB = 30 cm = 0.3 m;
• pA = 35 kPa; Q = 50 litre/sec = 0.05 m3/s;
• hf = 2 m of water; Direction of flow: from A to B

Department of Mechanical Engineering 193


Fluid Properties

• Water flows in a circular pipe. At one section the diameter is 0.3 m, the static pressure is 260 kPa gauge, the velocity is 3 m/s and the
elevation is 10 m above ground level. The elevation at a section downstream is 0 m, and the pipe diameter is 0.15 m. Find out the gauge
pressure at the downstream section. Frictional effects may be neglected. Assume density of water to be 999 kg/m3.

• Solution. Refer to Fig. 6.7. D1 = 0.3 m; D2 = 0.15 m; z1 = 0; z2 = 10 m; p1 = 260 kPa, V1 =


• 3 m/s; ρ = 999 kg/m3. From continuity equation, A1 V1 = A2V2,

Department of Mechanical Engineering 194


Fluid Properties

• A pipe 200 m long slopes down at 1 in 100 and tapers from 600 mm diameter at the higher end to 300 mm diameter at the lower end, and
carries 100 litres/sec of oil (sp. Gravity 0.8). If the pressure gauge at the higher end reads 60 kN/m2, determine: (i) Velocities at the two
ends; (ii) Pressure at the lower end. Neglect all losses.
• Solution. Length of the pipe, l = 200 m; diameter of the pipe at the higher end, D1 = 600 mm
• = 0.6 m,

• Rate of oil flow, Q = 100 litres/sec = 0.1 m3/s Pressure at the higher end, p1 = 60 kN/m2 (i) Velocities, V1, V2: Now, Q = A1 V1 = A2 V2
• where, V1 and V2 are the velocities at the higher and lower ends respectively.

• (ii) Pressure at the lower end p2:


• Using Bernoulli’s equation for both ends of pipe, we have:

Department of Mechanical Engineering 195


Fluid Properties

• Gasoline (sp. gr. 0.8) is flowing upwards a vertical pipeline which tapers from 300 mm to 150 mm diameter. A gasoline mercury differential
manometer is connected between 300 mm and 150 mm pipe section to measure the rate of flow. The distance between the manometer
tappings is 1 metre and gauge reading is 500 mm of mercury. Find: (i) Differential gauge reading in terms of gasoline head; (ii) Rate of flow.
Neglect friction and other losses between tappings.
• Solution. Sp. gravity of gasoline = 0.8
• At Inlet: Diameter, D1 = 300 mm = 0.3 m

(ii) Rate of flow, Q:


Let, V1 = Velocity of gasoline at the inlet, and
V2 = Velocity of gasoline at the outlet.
We know that, as per equation of continuity:
A1V1 = A2V2

Department of Mechanical Engineering 196


BERNOULLI’S EQUATION FOR REAL FLUID

• Bernoulli’s equation earlier derived was based on the assumption that fluid is non-viscous and therefore frictionless. Practically, all fluids
are real (and not ideal) and therefore are viscous as such there are always some losses in fluid flows. These losses have, therefore, to be
taken into consideration in the application of Bernoulli’s equation which gets modified (between sections 1 and 2) for real fluids as follows:

Department of Mechanical Engineering 197


Fluid Properties

• A drainage pump has tapered suction pipe. The pipe is running full of water. The pipe diameters at the inlet and at the upper end are 1 m
and 0.5 m respectively. The free water surface is 2 m above the centre of the inlet and centre of upper end is 3 m above the top of free
water surface. The pressure at the tip end of the pipe is 25 cm of mercury and it is known that loss of head by friction between top and the
bottom section is one-tenth of the velocity head at the top section. Compute the discharge in litre/sec. Neglect loss of head at the entrance
of the tapered pipe. (UPTU)

Department of Mechanical Engineering 198

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