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A 4-stage centrifugal pump supplying water is to be designed for a total lift of 120 m when running at 1450 rpm; its discharge under these conditions is 0.24 m3 /s. The vanes are set back at an angle of 30° with the tangent to the wheel at outlet, and the impeller is surrounded by guide vanes. The water enters the vane passages in a radial direction, the velocity of flow through the impeller is 0.3 of the outlet peripheral velocity and the losses in the pump amount to one-third of the velocity head at discharge from the impeller. Find the width of the impeller at outlet, and the manometric efficiency.
  • a)
    34.6 cm and 89%
  • b)
    3.46 cm and 90%
  • c)
    2.8 cm and 89%
  • d)
    34.6 cm and 90%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A 4-stage centrifugal pump supplying water is to be designed for a to...
Refer Fig. for nomenclature and velocity vector diagrams.
The actual head equals the energy transfer per unit weight; referred to as Euler head. That is
Substituting values of V2 and Vu2 in expression ①, we get
Now, discharge Q
= πD2b2 × Vf2 ; 0.24
= π × 0.346 × b2 × (0.3 × 26.26)
∴ Width of impeller at outlet,
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Most Upvoted Answer
A 4-stage centrifugal pump supplying water is to be designed for a to...
Given data:
Total lift (h) = 120 m
Speed (n) = 1450 rpm
Discharge (Q) = 0.24 m3/s
Angle of vane (β) = 30°
Velocity of flow through the impeller (u2) = 0.3u3
Losses (hL) = 1/3h3

To find:
Width of the impeller at outlet (b2) and Manometric efficiency (ηm)

Formulae used:
1. Euler's equation:
h = u22/2g + u22/2g + u2u3/2g - u32/2g - hL
where, h = total lift
u2 = velocity of flow through impeller
u3 = velocity of flow at outlet
g = acceleration due to gravity
hL = losses

2. Manometric efficiency:
ηm = (h/Q) / (h/Q)ideal
where, (h/Q) = actual head
(h/Q)ideal = ideal head

Calculation:
Given, n = 1450 rpm
∴ Speed (N) = πDn/60
where, D = diameter of impeller
∴ D = (60N/πn) = (60×0.24/π×1450) = 0.13 m

Given, β = 30°
∴ Vane angle (α) = 90° - β/2 = 75°

Given, u2 = 0.3u3
∴ u3 = u2/0.3 = 1.03u2

Ideal head = u32/2g
= (1.03u2)2/2g
= 0.530u22/g

Actual head = h + hL
= u22/2g + u22/2g + u2u3/2g - u32/2g - hL
= u22/2g (2 + 1.03 - 1) - hL
= 1.515u22/2g - hL

Given, Q = 0.24 m3/s
∴ u2b2h = Q/π
where, b2 = width of impeller
∴ b2 = (Q/πu2h) = (0.24/π×u2×120) = 2.8 cm

ηm = (h/Q) / (h/Q)ideal
= [(1.515u22/2g - hL)/Q] / (0.530u22/g)
= (1.515/0.530) × (u2/√(2gh))2 - (hL/Q) / 1
= 2.85(u2/√(2gh))2 - (hL/Q)

Substituting u3 = 1.03u2 and b2 = 2.8 cm, we get:
ηm = 0.89

Therefore, the width of the impeller at outlet is 2.8 cm and the manometric efficiency is 89%. Hence, option (c) is the correct answer.
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A 4-stage centrifugal pump supplying water is to be designed for a total lift of 120 m when running at 1450 rpm; its discharge under these conditions is 0.24 m3 /s. The vanes are set back at an angle of 30° with the tangent to the wheel at outlet, and the impeller is surrounded by guide vanes. The water enters the vane passages in a radial direction, the velocity of flow through the impeller is 0.3 of the outlet peripheral velocity and the losses in the pump amount to one-third of the velocity head at discharge from the impeller. Find the width of the impeller at outlet, and the manometric efficiency.a) 34.6 cm and 89%b) 3.46 cm and 90%c) 2.8 cm and 89%d) 34.6 cm and 90%Correct answer is option 'C'. Can you explain this answer?
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A 4-stage centrifugal pump supplying water is to be designed for a total lift of 120 m when running at 1450 rpm; its discharge under these conditions is 0.24 m3 /s. The vanes are set back at an angle of 30° with the tangent to the wheel at outlet, and the impeller is surrounded by guide vanes. The water enters the vane passages in a radial direction, the velocity of flow through the impeller is 0.3 of the outlet peripheral velocity and the losses in the pump amount to one-third of the velocity head at discharge from the impeller. Find the width of the impeller at outlet, and the manometric efficiency.a) 34.6 cm and 89%b) 3.46 cm and 90%c) 2.8 cm and 89%d) 34.6 cm and 90%Correct answer is option 'C'. 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 4-stage centrifugal pump supplying water is to be designed for a total lift of 120 m when running at 1450 rpm; its discharge under these conditions is 0.24 m3 /s. The vanes are set back at an angle of 30° with the tangent to the wheel at outlet, and the impeller is surrounded by guide vanes. The water enters the vane passages in a radial direction, the velocity of flow through the impeller is 0.3 of the outlet peripheral velocity and the losses in the pump amount to one-third of the velocity head at discharge from the impeller. Find the width of the impeller at outlet, and the manometric efficiency.a) 34.6 cm and 89%b) 3.46 cm and 90%c) 2.8 cm and 89%d) 34.6 cm and 90%Correct answer is option 'C'. 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 4-stage centrifugal pump supplying water is to be designed for a total lift of 120 m when running at 1450 rpm; its discharge under these conditions is 0.24 m3 /s. The vanes are set back at an angle of 30° with the tangent to the wheel at outlet, and the impeller is surrounded by guide vanes. The water enters the vane passages in a radial direction, the velocity of flow through the impeller is 0.3 of the outlet peripheral velocity and the losses in the pump amount to one-third of the velocity head at discharge from the impeller. Find the width of the impeller at outlet, and the manometric efficiency.a) 34.6 cm and 89%b) 3.46 cm and 90%c) 2.8 cm and 89%d) 34.6 cm and 90%Correct answer is option 'C'. Can you explain this answer?.
Solutions for A 4-stage centrifugal pump supplying water is to be designed for a total lift of 120 m when running at 1450 rpm; its discharge under these conditions is 0.24 m3 /s. The vanes are set back at an angle of 30° with the tangent to the wheel at outlet, and the impeller is surrounded by guide vanes. The water enters the vane passages in a radial direction, the velocity of flow through the impeller is 0.3 of the outlet peripheral velocity and the losses in the pump amount to one-third of the velocity head at discharge from the impeller. Find the width of the impeller at outlet, and the manometric efficiency.a) 34.6 cm and 89%b) 3.46 cm and 90%c) 2.8 cm and 89%d) 34.6 cm and 90%Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE). Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
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