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A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.
Correct answer is 'Range: 301 to 302'. Can you explain this answer?
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A pipe 10 cm in diameter and 1000 m long is used to pump oil of visco...
Discharge, Q = 1200 litre⁄min
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Viscosity, μ = 8.5 poise = 8.5 × 0.1 = 0.85 N s⁄m
Flow velocity = discharge / area
= 275.78
Since the Reynolds number is less than 2000, the flow is laminar. For laminar flow, the friction coefficient is given by
Head loss due to friction in 1000 m length of pipe
The pressure to be developed by the pump can be worked out by applying Bernoulli’s equation between the pump outlet (suffix 1) and the end of the pipeline (suffix 2)
With horizontal line through the pump center,
y1 = 0
and y2 = 300 sin 10° + 700 sin 15° = 233.25 m p2 = 0 as the pressure at the pipe exit is atmospheric Also V1 = V2
∴p1 / w = 233.25 + 768
= 1001.25 m of oil
Power required to develop this pressure
= w Q H
= (0.92 × 1000 × 9.81) × 0.02 × 1001.25
= 180729 Nm⁄s ≈ 180.73 kW
Power of driving motor
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A pipe 10 cm in diameter and 1000 m long is used to pump oil of visco...
Calculation of Power Required to Drive the Pump
Given data:
- Diameter of the pipe (D) = 10 cm = 0.1 m
- Length of the pipe (L) = 1000 m
- Viscosity of oil (μ) = 3.5 poise = 0.35 Pa s
- Specific gravity of oil (SG) = 0.92
- Flow rate of oil (Q) = 1200 litre/min = 0.02 m^3/s
- Pipe slope for the first 300 m (θ1) = 10°
- Pipe slope for the remaining 700 m (θ2) = 15°
- Pump efficiency (η) = 60%
Assumptions:
- The fluid flow is laminar
- The pipe is smooth and new
- The fittings and valves in the pipe are negligible
- The fluid is incompressible
- The gravitational acceleration is 9.81 m/s^2
- The friction factor (f) is constant and can be determined using the Darcy-Weisbach equation
Head Loss Calculation:
- Calculate the Reynolds number (Re) using the formula:
Re = (4Q)/(πDμ)
Re = (4×0.02)/(π×0.1×0.35)
Re = 182.7 (laminar flow)
- Calculate the friction factor (f) using the Darcy-Weisbach equation:
f = 64/Re
f = 64/182.7
f = 0.35
- Calculate the head loss due to friction (hf) using the Darcy-Weisbach equation:
hf = (fL/D)(V^2/2g)
hf = ((0.35×1000)/0.1)(0.02^2/2×9.81)
hf = 6.68 m
- Calculate the head loss due to elevation (he) for the first 300 m of pipe:
he = L1sinθ1
he = 300sin10°
he = 52.1 m
- Calculate the head loss due to elevation (he) for the remaining 700 m of pipe:
he = L2sinθ2
he = 700sin15°
he = 191.4 m
- Total head loss (ht) = hf + he1 + he2
ht = 6.68 + 52.1 + 191.4
ht = 250.18 m
Power Calculation:
- Calculate the power required to drive the pump (P) using the formula:
P = (γQht)/(η)
γ = SG×ρwater×g
ρwater = 1000 kg/m^3 (density of water at 4°C)
g = 9.81 m/s^2
γ = 0.92×1000×9.81
γ = 9058.92 N/m^3
P = (9058.92×0.02×250.18)/(0.6×1000)
P = 302.01 kW
Therefore, the power required to drive the pump is 302.01 kW (approximated to the nearest integer, i
Given data:
- Diameter of the pipe (D) = 10 cm = 0.1 m
- Length of the pipe (L) = 1000 m
- Viscosity of oil (μ) = 3.5 poise = 0.35 Pa s
- Specific gravity of oil (SG) = 0.92
- Flow rate of oil (Q) = 1200 litre/min = 0.02 m^3/s
- Pipe slope for the first 300 m (θ1) = 10°
- Pipe slope for the remaining 700 m (θ2) = 15°
- Pump efficiency (η) = 60%
Assumptions:
- The fluid flow is laminar
- The pipe is smooth and new
- The fittings and valves in the pipe are negligible
- The fluid is incompressible
- The gravitational acceleration is 9.81 m/s^2
- The friction factor (f) is constant and can be determined using the Darcy-Weisbach equation
Head Loss Calculation:
- Calculate the Reynolds number (Re) using the formula:
Re = (4Q)/(πDμ)
Re = (4×0.02)/(π×0.1×0.35)
Re = 182.7 (laminar flow)
- Calculate the friction factor (f) using the Darcy-Weisbach equation:
f = 64/Re
f = 64/182.7
f = 0.35
- Calculate the head loss due to friction (hf) using the Darcy-Weisbach equation:
hf = (fL/D)(V^2/2g)
hf = ((0.35×1000)/0.1)(0.02^2/2×9.81)
hf = 6.68 m
- Calculate the head loss due to elevation (he) for the first 300 m of pipe:
he = L1sinθ1
he = 300sin10°
he = 52.1 m
- Calculate the head loss due to elevation (he) for the remaining 700 m of pipe:
he = L2sinθ2
he = 700sin15°
he = 191.4 m
- Total head loss (ht) = hf + he1 + he2
ht = 6.68 + 52.1 + 191.4
ht = 250.18 m
Power Calculation:
- Calculate the power required to drive the pump (P) using the formula:
P = (γQht)/(η)
γ = SG×ρwater×g
ρwater = 1000 kg/m^3 (density of water at 4°C)
g = 9.81 m/s^2
γ = 0.92×1000×9.81
γ = 9058.92 N/m^3
P = (9058.92×0.02×250.18)/(0.6×1000)
P = 302.01 kW
Therefore, the power required to drive the pump is 302.01 kW (approximated to the nearest integer, i
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A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer?
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A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer?.
A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer?.
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A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer?, a detailed solution for A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer? has been provided alongside types of A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A pipe 10 cm in diameter and 1000 m long is used to pump oil of viscosity 3.5 poise and specific gravity 0.92 at the rate of 1200 litre/min. The first 300 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and the remaining pipe is laid to the ground sloping upwards at 15° to the horizontal. Determine the power (in kW) of the driving motor if the pump efficiency is 60 percent. Assume suitable data for friction coefficient f, if required.Correct answer is 'Range: 301 to 302'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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