For fluid undergoing circular motion, the centripetal force is provided by a pressure difference. Consider a fluid element (density p) at radial distance r, which has thickness dr in the radial direction and surface area dA normal to the radial direction. The pressure difference gives rise to a force on the fluid element equal to (p(r + dr) – p(r))dA. (i) Equating the pressure difference to the centripetal force, find an expression for the radial pressure gradient in terms of p, r, and fluid velocity v.

For fluid undergoing circular motion, the centripetal force is provided by a pressure difference. Consider a fluid element (density p) at radial distance r, which has thickness dr in the radial direction and surface area dA normal to the radial direction. The pressure difference gives rise to a force on the fluid element equal to (p(r + dr) – p(r))dA. (i) Equating the pressure difference to the centripetal force, find an expression for the radial pressure gradient in terms of p, r, and fluid velocity v.

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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Pressure and Stress

Question

For fluid undergoing circular motion, the centripetal force is provided by a pressure difference.
Consider a fluid element (density p) at radial distance r, which has thickness dr in the radial direction
and surface area dA normal to the radial direction. The pressure difference gives rise to a force on the
fluid element equal to (p(r + dr) – p(r))dA.
(i) Equating the pressure difference to the centripetal force, find an expression for the radial
pressure gradient in terms of p, r, and fluid velocity v.
(ii) A fluid is undergoing body rotation in the r-0 plane (cylindrical polar co-ordinates). By
considering the gravitational pressure head, show that the shape of a free surface z(r) is
parabolic.
(iii) Find and sketch a similar expression for the free surface of a fluid vortex produced by a
rotating cylindrical spindle (i.e. a solid cylindrical rod) of radius Ro.

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