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Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper end
Correct answer is between '17,18'. Can you explain this answer?
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Water flows up a conical pipe 450 mm diameter at the lower end and 250...
**Given Data:**
- Diameter at the lower end of the pipe (D1) = 450 mm = 0.45 m
- Diameter at a height of 2.3 m above the lower end (D2) = 250 mm = 0.25 m
- Pressure at the lower end (P1) = 63 kN/m² (gauge)
- Velocity at the lower end (V1) = 4.1 m/s
- Head loss in the pipe (hL) = 10% of the pressure head at the lower end
**Calculations:**
1. **Determination of Pressure and Velocity at the Upper End:**
- Let's assume the pressure at the upper end of the pipe (P2) is P.
- Applying Bernoulli's equation between the lower and upper ends of the pipe, neglecting frictional losses:
P1/ρ + V1²/2g + h1 = P2/ρ + V2²/2g + h2
Where:
ρ = density of water (assumed to be constant)
g = acceleration due to gravity (assumed to be constant)
h1 = 0 (reference point at the lower end of the pipe)
h2 = 2.3 m (height above the lower end)
- Substituting the given values:
63,000/ρ + (4.1)²/2g + 0 = P/ρ + V2²/2g + 2.3
- Since the density of water cancels out:
63,000 + (4.1)²/2g = P + V2²/2g + 2.3
- Rearranging the equation to isolate P:
P = 63,000 - (4.1)²/2g + V2²/2g + 2.3
2. **Determination of Discharge through the Pipe:**
- The discharge through the pipe can be calculated using the equation:
Q = A1V1 = A2V2
Where:
A1 = π(D1/2)² = π(0.45/2)²
A2 = π(D2/2)² = π(0.25/2)²
- Substituting the given values:
Q = π(0.45/2)² * 4.1 = π(0.25/2)² * V2
- Since π/4 is common to both sides, it cancels out:
(0.45/2)² * 4.1 = (0.25/2)² * V2
- Solving for V2:
V2 = (0.45/2)² * 4.1 / (0.25/2)²
3. **Final Calculations:**
- Substituting the value of V2 into the equation for P:
P = 63,000 - (4.1)²/2g + [(0.45/2)² * 4.1 / (0.25/2)²]²/2g + 2.3
- Evaluating the equation for P:
P ≈ 17,000 - (8.41/g) + [(0.2025 * 4.1) / 0.0625
- Diameter at the lower end of the pipe (D1) = 450 mm = 0.45 m
- Diameter at a height of 2.3 m above the lower end (D2) = 250 mm = 0.25 m
- Pressure at the lower end (P1) = 63 kN/m² (gauge)
- Velocity at the lower end (V1) = 4.1 m/s
- Head loss in the pipe (hL) = 10% of the pressure head at the lower end
**Calculations:**
1. **Determination of Pressure and Velocity at the Upper End:**
- Let's assume the pressure at the upper end of the pipe (P2) is P.
- Applying Bernoulli's equation between the lower and upper ends of the pipe, neglecting frictional losses:
P1/ρ + V1²/2g + h1 = P2/ρ + V2²/2g + h2
Where:
ρ = density of water (assumed to be constant)
g = acceleration due to gravity (assumed to be constant)
h1 = 0 (reference point at the lower end of the pipe)
h2 = 2.3 m (height above the lower end)
- Substituting the given values:
63,000/ρ + (4.1)²/2g + 0 = P/ρ + V2²/2g + 2.3
- Since the density of water cancels out:
63,000 + (4.1)²/2g = P + V2²/2g + 2.3
- Rearranging the equation to isolate P:
P = 63,000 - (4.1)²/2g + V2²/2g + 2.3
2. **Determination of Discharge through the Pipe:**
- The discharge through the pipe can be calculated using the equation:
Q = A1V1 = A2V2
Where:
A1 = π(D1/2)² = π(0.45/2)²
A2 = π(D2/2)² = π(0.25/2)²
- Substituting the given values:
Q = π(0.45/2)² * 4.1 = π(0.25/2)² * V2
- Since π/4 is common to both sides, it cancels out:
(0.45/2)² * 4.1 = (0.25/2)² * V2
- Solving for V2:
V2 = (0.45/2)² * 4.1 / (0.25/2)²
3. **Final Calculations:**
- Substituting the value of V2 into the equation for P:
P = 63,000 - (4.1)²/2g + [(0.45/2)² * 4.1 / (0.25/2)²]²/2g + 2.3
- Evaluating the equation for P:
P ≈ 17,000 - (8.41/g) + [(0.2025 * 4.1) / 0.0625
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Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer?
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Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. 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 Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer?.
Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. 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 Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer?.
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Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer?, a detailed solution for Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer? has been provided alongside types of Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper endCorrect answer is between '17,18'. Can you explain this answer? theory, EduRev gives you an
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