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A fluid of density p is rotating with constant angular velocity w about the central vertical axis of a cylindrical container. (a) Show that the variation in pressure in the radial direction is given by dP = pw²r. dr (b) If the pressure is at the axis of rotation (r = 0) is Pc, show that the pressure P(r) at any point r is given by P(r) = P. + 5pa?r?.

A fluid of density p is rotating with constant angular velocity w about the central vertical axis of a cylindrical container. (a) Show that the variation in pressure in the radial direction is given by dP = pw²r. dr (b) If the pressure is at the axis of rotation (r = 0) is Pc, show that the pressure P(r) at any point r is given by P(r) = P. + 5pa?r?.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A fluid of density p is rotating with constant angular velocity w about the central vertical axis of a cylindrical container. (a) Show that the variation in pressure in the radial direction is given by dP = pwr. dr (b) If the pressure is at the axis of rotation (r = 0) is Pc, show that the pressure P(r) at any point r is given by 1 P(r) = P. + pw²r?. (c) Show that the liquid surface is a paraboloid: the horizontal cross section of the liquid is a circle and the vertical cross section is a parabola given by w?r2 y = 2g Note: This is a “problem to prove." Your objective is to construct a proof or rational argument based on principles of physics and mathematics that connect given or known information to the stated result. r
Transcribed Image Text:A fluid of density p is rotating with constant angular velocity w about the central vertical axis of a cylindrical container. (a) Show that the variation in pressure in the radial direction is given by dP = pwr. dr (b) If the pressure is at the axis of rotation (r = 0) is Pc, show that the pressure P(r) at any point r is given by 1 P(r) = P. + pw²r?. (c) Show that the liquid surface is a paraboloid: the horizontal cross section of the liquid is a circle and the vertical cross section is a parabola given by w?r2 y = 2g Note: This is a “problem to prove." Your objective is to construct a proof or rational argument based on principles of physics and mathematics that connect given or known information to the stated result. r
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