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The discharge of a centrifugal pump is 25 L s-1 against the delivery head of 10 m. The outlet of the delivery pipe is submerged. A 200 m long 100 mm diameter pipe is connected with the delivery end of the pump. The friction factor for the pipe is 0.03. The minor losses in the delivery pipe are 1 m. The pressure at the delivery end of the pump in kPa is __________
Correct answer is between '411.5,412.5'. Can you explain this answer?
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The discharge of a centrifugal pump is 25 L s-1against the delivery he...
Given:
- Discharge of the centrifugal pump (Q) = 25 L/s = 0.025 m³/s
- Delivery head (H) = 10 m
- Length of the pipe (L) = 200 m
- Diameter of the pipe (D) = 100 mm = 0.1 m
- Friction factor (f) = 0.03
- Minor losses in the delivery pipe (Σh) = 1 m
To Find:
- Pressure at the delivery end of the pump (P) in kPa
Assumptions:
- The flow is steady and incompressible.
- The fluid is water.
Solution:
Step 1: Calculate the velocity of flow at the delivery end of the pump
- The velocity of flow (V) can be calculated using the formula:
V = Q / A
where A is the cross-sectional area of the pipe.
- The cross-sectional area of the pipe (A) can be calculated using the formula:
A = π * (D/2)²
- Substituting the given values:
A = π * (0.1/2)² = 0.00785 m²
- Substituting the values of Q and A, we can calculate V:
V = 0.025 / 0.00785 = 3.18 m/s
Step 2: Calculate the Reynolds number (Re)
- Reynolds number (Re) can be calculated using the formula:
Re = (V * D) / ν
where ν is the kinematic viscosity of water.
- For water at room temperature, the kinematic viscosity (ν) is approximately 10^-6 m²/s.
- Substituting the given values:
Re = (3.18 * 0.1) / 10^-6 = 3.18 * 10^7
Step 3: Calculate the frictional losses (hf)
- Frictional losses (hf) can be calculated using the Darcy-Weisbach equation:
hf = (f * L * V²) / (2 * D)
- Substituting the given values:
hf = (0.03 * 200 * 3.18²) / (2 * 0.1) = 12.0764 m
Step 4: Calculate the total head (Ht)
- The total head (Ht) is the sum of the delivery head (H), frictional losses (hf), and minor losses (Σh).
- Ht = H + hf + Σh
- Substituting the given values:
Ht = 10 + 12.0764 + 1 = 23.0764 m
Step 5: Calculate the pressure at the delivery end of the pump (P)
- The pressure (P) can be calculated using the formula:
P = ρ * g * Ht
where ρ is the density of water and g is the acceleration due to gravity.
- For water at room temperature, the density (ρ) is approximately 1000 kg/m³ and the acceleration due to gravity (g) is approximately
- Discharge of the centrifugal pump (Q) = 25 L/s = 0.025 m³/s
- Delivery head (H) = 10 m
- Length of the pipe (L) = 200 m
- Diameter of the pipe (D) = 100 mm = 0.1 m
- Friction factor (f) = 0.03
- Minor losses in the delivery pipe (Σh) = 1 m
To Find:
- Pressure at the delivery end of the pump (P) in kPa
Assumptions:
- The flow is steady and incompressible.
- The fluid is water.
Solution:
Step 1: Calculate the velocity of flow at the delivery end of the pump
- The velocity of flow (V) can be calculated using the formula:
V = Q / A
where A is the cross-sectional area of the pipe.
- The cross-sectional area of the pipe (A) can be calculated using the formula:
A = π * (D/2)²
- Substituting the given values:
A = π * (0.1/2)² = 0.00785 m²
- Substituting the values of Q and A, we can calculate V:
V = 0.025 / 0.00785 = 3.18 m/s
Step 2: Calculate the Reynolds number (Re)
- Reynolds number (Re) can be calculated using the formula:
Re = (V * D) / ν
where ν is the kinematic viscosity of water.
- For water at room temperature, the kinematic viscosity (ν) is approximately 10^-6 m²/s.
- Substituting the given values:
Re = (3.18 * 0.1) / 10^-6 = 3.18 * 10^7
Step 3: Calculate the frictional losses (hf)
- Frictional losses (hf) can be calculated using the Darcy-Weisbach equation:
hf = (f * L * V²) / (2 * D)
- Substituting the given values:
hf = (0.03 * 200 * 3.18²) / (2 * 0.1) = 12.0764 m
Step 4: Calculate the total head (Ht)
- The total head (Ht) is the sum of the delivery head (H), frictional losses (hf), and minor losses (Σh).
- Ht = H + hf + Σh
- Substituting the given values:
Ht = 10 + 12.0764 + 1 = 23.0764 m
Step 5: Calculate the pressure at the delivery end of the pump (P)
- The pressure (P) can be calculated using the formula:
P = ρ * g * Ht
where ρ is the density of water and g is the acceleration due to gravity.
- For water at room temperature, the density (ρ) is approximately 1000 kg/m³ and the acceleration due to gravity (g) is approximately
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The discharge of a centrifugal pump is 25 L s-1against the delivery head of 10 m. The outlet of the delivery pipe is submerged. A 200 m long 100 mm diameter pipe is connected with the delivery end of the pump. The friction factor for the pipe is 0.03. The minor losses in the delivery pipe are 1 m. The pressure at the delivery end of the pump in kPa is __________Correct answer is between '411.5,412.5'. Can you explain this answer?
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The discharge of a centrifugal pump is 25 L s-1against the delivery head of 10 m. The outlet of the delivery pipe is submerged. A 200 m long 100 mm diameter pipe is connected with the delivery end of the pump. The friction factor for the pipe is 0.03. The minor losses in the delivery pipe are 1 m. The pressure at the delivery end of the pump in kPa is __________Correct answer is between '411.5,412.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The discharge of a centrifugal pump is 25 L s-1against the delivery head of 10 m. The outlet of the delivery pipe is submerged. A 200 m long 100 mm diameter pipe is connected with the delivery end of the pump. The friction factor for the pipe is 0.03. The minor losses in the delivery pipe are 1 m. The pressure at the delivery end of the pump in kPa is __________Correct answer is between '411.5,412.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The discharge of a centrifugal pump is 25 L s-1against the delivery head of 10 m. The outlet of the delivery pipe is submerged. A 200 m long 100 mm diameter pipe is connected with the delivery end of the pump. The friction factor for the pipe is 0.03. The minor losses in the delivery pipe are 1 m. The pressure at the delivery end of the pump in kPa is __________Correct answer is between '411.5,412.5'. Can you explain this answer?.
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