A fluid flowing steadily in a circular pipe of radiusR has a velocity that is everywhere parallel to theaxis (centreline) of the pipe. The velocitydistribution along the radial direction isV₁ = U(1-1²2).where r is the radial distance asmeasured from the pipe axis and U is themaximum velocity at r = 0. The average velocityof the fluid in the pipe is

This question has been taken from fluid mechanics and the explanation is given below:

Answered: maximum velocity at r = 0. The average…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters di and d2 (where d₁ = 4d₂) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is
A U-tube of uniform cross-section has both arms open to the atmosphere. The U-tube contains three immiscible liquids, with density PA, PB, and pc, as depicted in the diagram below, where po is the atmospheric pressure. We denote h to be the depth of the open surface of liquid A on the left arm, relative to the open surface of liquid Con the right arm. I is the depth of the interface between liquid B and C on the right arm and 2l is the depth of the interface between liquid A and liquid B on the right arm. Po PA (c) Po PC PB е е (a) Explain why the liquid densities need to satisfy the condition PA PB PC. (b) Write down an expression for the pressure at depth z below the surface of liquid A in the left-hand part of the tube. Show that l < h < 2l if PB + PC < PA•

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maximum velocity at r = 0. The average velocity of the fluid in the pipe is