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A laminar fluid is flowing through a circular pipe of radius 78 mm. Find the radical distance (in mm) measured from the centre where the average velocity is indicated as the local velocity. (Answer up to two decimal places)
Correct answer is '55.38'. Can you explain this answer?
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A laminar fluid is flowing through a circular pipe of radius 78 mm. F...
Understanding the problem:
Given data:
- Radius of the circular pipe (r) = 78 mm
- Local velocity = Average velocity
Solution:
Step 1: Finding the local velocity
- In laminar flow through a pipe, the average velocity (V_avg) is equal to the maximum velocity at the center of the pipe (V_max).
- The local velocity (V) is given by the formula V = V_avg = V_max.
Step 2: Finding the radial distance where the local velocity is indicated
- In laminar flow through a circular pipe, the velocity profile is parabolic.
- The velocity profile is given by the formula V(r) = (2/3)V_avg * (1 - (r/R)^2), where r is the radial distance from the center.
- At the center of the pipe (r = 0), the velocity is maximum (V_max = V_avg).
- To find the radial distance where the local velocity is indicated, we need to solve for r when V(r) = V_avg.
Step 3: Calculating the radial distance
- Substituting V_avg for V in the velocity profile equation:
V_avg = (2/3)V_avg * (1 - (r/R)^2)
1 = (2/3)(1 - (r/R)^2)
1 = 2/3 - 2r^2/(3R^2)
2/3 = 2r^2/(3R^2)
r^2 = R^2 / 3
r = R / sqrt(3) = 78 / sqrt(3) mm
- Calculating the numerical value:
r ≈ 78 / 1.732 ≈ 45.06 mm
Therefore, the radial distance from the center where the average velocity is indicated as the local velocity is approximately 45.06 mm.
Given data:
- Radius of the circular pipe (r) = 78 mm
- Local velocity = Average velocity
Solution:
Step 1: Finding the local velocity
- In laminar flow through a pipe, the average velocity (V_avg) is equal to the maximum velocity at the center of the pipe (V_max).
- The local velocity (V) is given by the formula V = V_avg = V_max.
Step 2: Finding the radial distance where the local velocity is indicated
- In laminar flow through a circular pipe, the velocity profile is parabolic.
- The velocity profile is given by the formula V(r) = (2/3)V_avg * (1 - (r/R)^2), where r is the radial distance from the center.
- At the center of the pipe (r = 0), the velocity is maximum (V_max = V_avg).
- To find the radial distance where the local velocity is indicated, we need to solve for r when V(r) = V_avg.
Step 3: Calculating the radial distance
- Substituting V_avg for V in the velocity profile equation:
V_avg = (2/3)V_avg * (1 - (r/R)^2)
1 = (2/3)(1 - (r/R)^2)
1 = 2/3 - 2r^2/(3R^2)
2/3 = 2r^2/(3R^2)
r^2 = R^2 / 3
r = R / sqrt(3) = 78 / sqrt(3) mm
- Calculating the numerical value:
r ≈ 78 / 1.732 ≈ 45.06 mm
Therefore, the radial distance from the center where the average velocity is indicated as the local velocity is approximately 45.06 mm.
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Community Answer
A laminar fluid is flowing through a circular pipe of radius 78 mm. F...
Given: R = 78 mm
Radical distance measured from the centre where the average velocity is indicated as the local velocity is,
D = 0.71R
= 0.71(78)
= 55.38 mm
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A laminar fluid is flowing through a circular pipe of radius 78 mm. Find the radical distance (in mm) measured from the centre where the average velocity is indicated as the local velocity. (Answer up to two decimal places)Correct answer is '55.38'. Can you explain this answer?
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