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Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe?
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Show that for steady laminar flow through circular pipe mean velocity ...
Introduction:
Steady laminar flow through circular pipe is an important topic in fluid mechanics. In this process, fluid flows through a circular pipe with a constant velocity. The mean velocity of flow occurs at a radial distance of 0.707R from the center of the pipe where R is the radius of the pipe. In this article, we will explain this concept in detail.
Derivation:
The velocity distribution in a circular pipe can be represented by the following equation:
u(r) = 2 * Vmax * (1 - (r/R)^2)
Where u(r) is the velocity at a radial distance of r from the center of the pipe, Vmax is the maximum velocity at the center of the pipe, and R is the radius of the pipe.
To find the mean velocity of flow, we need to integrate the velocity distribution equation over the entire cross-section of the pipe.
∫(0 to R) u(r) * 2πr dr = Q/πR^2
Where Q is the volumetric flow rate.
Simplifying the above equation, we get:
Vmean = (2/3) * Vmax
Where Vmean is the mean velocity of flow.
To find the radial distance at which the mean velocity occurs, we need to substitute Vmean in the velocity distribution equation and solve for r.
Vmean = 2 * Vmax * (1 - (r/R)^2)
(2/3) * Vmax = 2 * Vmax * (1 - (r/R)^2)
1/3 = (r/R)^2
r/R = 0.577 or 0.707
Therefore, the mean velocity of flow occurs at a radial distance of 0.707R from the center of the pipe.
Conclusion:
In conclusion, the mean velocity of flow through a circular pipe occurs at a radial distance of 0.707R from the center of the pipe. This concept is important in fluid mechanics and is used in various applications such as flow measurement and pipe design.
Steady laminar flow through circular pipe is an important topic in fluid mechanics. In this process, fluid flows through a circular pipe with a constant velocity. The mean velocity of flow occurs at a radial distance of 0.707R from the center of the pipe where R is the radius of the pipe. In this article, we will explain this concept in detail.
Derivation:
The velocity distribution in a circular pipe can be represented by the following equation:
u(r) = 2 * Vmax * (1 - (r/R)^2)
Where u(r) is the velocity at a radial distance of r from the center of the pipe, Vmax is the maximum velocity at the center of the pipe, and R is the radius of the pipe.
To find the mean velocity of flow, we need to integrate the velocity distribution equation over the entire cross-section of the pipe.
∫(0 to R) u(r) * 2πr dr = Q/πR^2
Where Q is the volumetric flow rate.
Simplifying the above equation, we get:
Vmean = (2/3) * Vmax
Where Vmean is the mean velocity of flow.
To find the radial distance at which the mean velocity occurs, we need to substitute Vmean in the velocity distribution equation and solve for r.
Vmean = 2 * Vmax * (1 - (r/R)^2)
(2/3) * Vmax = 2 * Vmax * (1 - (r/R)^2)
1/3 = (r/R)^2
r/R = 0.577 or 0.707
Therefore, the mean velocity of flow occurs at a radial distance of 0.707R from the center of the pipe.
Conclusion:
In conclusion, the mean velocity of flow through a circular pipe occurs at a radial distance of 0.707R from the center of the pipe. This concept is important in fluid mechanics and is used in various applications such as flow measurement and pipe design.
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Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe?
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Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe?.
Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that for steady laminar flow through circular pipe mean velocity of flow occurs at radial distance of 0.707R from the Centre of pipe where R is radius of pipe?.
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