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The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm respectively. Find the discharge through pipe if the velocity of water flowing through the pipe at section 1 is 6 m/s. Determine also the velocity at section 2.
- a)2.27 m/s
- b)4.54 m/s
- c)1.13 m/s
- d)3.25 m/s
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm res...
Explanation: According to continuity equation,
Area × velocity = constant
Area1*Velocity1 = Area2*Velocity2
Velocity2=(Area1*Velocity1)/Area2
= (82 * 6) / 132=2.27 m/s.
Area × velocity = constant
Area1*Velocity1 = Area2*Velocity2
Velocity2=(Area1*Velocity1)/Area2
= (82 * 6) / 132=2.27 m/s.
Most Upvoted Answer
The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm res...
Given:
Diameter at section 1 = 8 cm
Diameter at section 2 = 13 cm
Velocity at section 1 = 6 m/s
To find:
Discharge through the pipe and velocity at section 2
Solution:
We know that the discharge (Q) through a pipe is given by the formula:
Q = Av
where A is the cross-sectional area of the pipe and v is the velocity of water flowing through the pipe.
Cross-sectional area at section 1:
A1 = π/4 * (8 cm)^2 = 50.27 cm^2
Cross-sectional area at section 2:
A2 = π/4 * (13 cm)^2 = 132.73 cm^2
Velocity at section 2 can be found using the continuity equation, which states that the mass flow rate of a fluid is constant, i.e.:
m_dot = ρAV = constant
where ρ is the density of water.
Since the pipe is horizontal and the diameter is changing, we can assume that the pressure at section 1 and section 2 is the same. Therefore, we can write:
ρ1A1v1 = ρ2A2v2
where v1 and v2 are the velocities at section 1 and section 2 respectively.
We can rearrange the equation to find v2:
v2 = (A1/A2) * v1
Substituting the values, we get:
v2 = (50.27/132.73) * 6 m/s = 2.27 m/s
Now, we can find the discharge through the pipe at section 1:
Q = A1 * v1 = 50.27 cm^2 * 6 m/s = 3.0162 m^3/s
Therefore, the correct answer is option A) 2.27 m/s.
Diameter at section 1 = 8 cm
Diameter at section 2 = 13 cm
Velocity at section 1 = 6 m/s
To find:
Discharge through the pipe and velocity at section 2
Solution:
We know that the discharge (Q) through a pipe is given by the formula:
Q = Av
where A is the cross-sectional area of the pipe and v is the velocity of water flowing through the pipe.
Cross-sectional area at section 1:
A1 = π/4 * (8 cm)^2 = 50.27 cm^2
Cross-sectional area at section 2:
A2 = π/4 * (13 cm)^2 = 132.73 cm^2
Velocity at section 2 can be found using the continuity equation, which states that the mass flow rate of a fluid is constant, i.e.:
m_dot = ρAV = constant
where ρ is the density of water.
Since the pipe is horizontal and the diameter is changing, we can assume that the pressure at section 1 and section 2 is the same. Therefore, we can write:
ρ1A1v1 = ρ2A2v2
where v1 and v2 are the velocities at section 1 and section 2 respectively.
We can rearrange the equation to find v2:
v2 = (A1/A2) * v1
Substituting the values, we get:
v2 = (50.27/132.73) * 6 m/s = 2.27 m/s
Now, we can find the discharge through the pipe at section 1:
Q = A1 * v1 = 50.27 cm^2 * 6 m/s = 3.0162 m^3/s
Therefore, the correct answer is option A) 2.27 m/s.
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The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm respectively. Find the discharge through pipe if the velocity of water flowing through the pipe at section 1 is 6 m/s. Determine also the velocity at section 2.a)2.27 m/sb)4.54 m/sc)1.13 m/sd)3.25 m/sCorrect answer is option 'A'. Can you explain this answer?
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The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm respectively. Find the discharge through pipe if the velocity of water flowing through the pipe at section 1 is 6 m/s. Determine also the velocity at section 2.a)2.27 m/sb)4.54 m/sc)1.13 m/sd)3.25 m/sCorrect answer is option 'A'. 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 The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm respectively. Find the discharge through pipe if the velocity of water flowing through the pipe at section 1 is 6 m/s. Determine also the velocity at section 2.a)2.27 m/sb)4.54 m/sc)1.13 m/sd)3.25 m/sCorrect answer is option 'A'. 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 The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm respectively. Find the discharge through pipe if the velocity of water flowing through the pipe at section 1 is 6 m/s. Determine also the velocity at section 2.a)2.27 m/sb)4.54 m/sc)1.13 m/sd)3.25 m/sCorrect answer is option 'A'. Can you explain this answer?.
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