(5) Derive the continuity equation in spherical coordinates in two ways. (i) Starting from first principles using an infinitesimal control volume fixed in space. To do this, set up a small elemental control volume in the spherical coordinate system, and identify the rates of inflow/outflow of mass through each face of the control volume; setting the net inflow equal to the rate of mass accumulation in the element. (ii) Starting from the vector form of the continuity equation derived in the course note and using the divergence and/or gradient operators for spherical coordinates.

(5) Derive the continuity equation in spherical coordinates in two ways. (i) Starting from first principles using an infinitesimal control volume fixed in space. To do this, set up a small elemental control volume in the spherical coordinate system, and identify the rates of inflow/outflow of mass through each face of the control volume; setting the net inflow equal to the rate of mass accumulation in the element. (ii) Starting from the vector form of the continuity equation derived in the course note and using the divergence and/or gradient operators for spherical coordinates.

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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Highway Drainage

Highway drainage is the process of extracting and regulating the excess surface water on the pavement by giving the desired slope. The construction of a highway drain helps to divert the water present on the surface, and sub-grade by the means of slope. Highway drainage systems are a necessary part of smooth functioning of traffic, since the highway drainage systems provide proper disposal of unwanted substances from the highways.

Question

(5) Derive the continuity equation in spherical coordinates in two ways. (i) Starting
from first principles using an infinitesimal control volume fixed in space. To do
this, set up a small elemental control volume in the spherical coordinate system,
and identify the rates of inflow/outflow of mass through each face of the control
volume; setting the net inflow equal to the rate of mass accumulation in the
element. (ii) Starting from the vector form of the continuity equation derived in
the course note and using the divergence and/or gradient operators for spherical
coordinates.

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