Question

Q1 The governing principles in fluid mechanics are the conservation laws for mass, momentum, and energy. These can be stated either in integral form when applied to an extended region, or in differential form when applied to a fluid particle or to an infinitesimal control volume. (a) Write in words the conservation law of mass and derive its analytical expression based on an infinitesimal cubical control volume in a Cartesian coordinate system, given a generic velocity flow field V=(u,v,w). [5] (b) The lumbar puncture is a common procedure in hospitals where the pressure within the spinal canal is usually measured and some cerebrospinal fluid (CSF) is removed either to reduce the pressure or for a sample to be sent for testing. Write a description of how the lumbar puncture is carried out and list some conditions that could be diagnosed by testing the CSF. [5] (c) Write down the equation of conservation of linear momentum and describe in words the meaning of each term appearing into the equation. [5] (d) Simplify the equation of conservation of linear momentum to express the body pressure as function of the CSF height within the piezometer tube connected to the spinal canal. [5]

          Q1
The governing principles in fluid mechanics are the conservation laws for
mass, momentum, and energy. These can be stated either in integral form
when applied to an extended region, or in differential form when applied to a
fluid particle or to an infinitesimal control volume.
(a)
Write in words the conservation law of mass and derive its analytical
expression based on an infinitesimal cubical control volume in a Cartesian
coordinate system, given a generic velocity flow field V=(u,v,w).
[5]
(b)
The lumbar puncture is a common procedure in hospitals where the pressure
within the spinal canal is usually measured and some cerebrospinal fluid
(CSF) is removed either to reduce the pressure or for a sample to be sent for
testing. Write a description of how the lumbar puncture is carried out and list
some conditions that could be diagnosed by testing the CSF.
[5]
(c)
Write down the equation of conservation of linear momentum and describe in
words the meaning of each term appearing into the equation.
[5]
(d)
Simplify the equation of conservation of linear momentum to express the body
pressure as function of the CSF height within the piezometer tube connected
to the spinal canal.
[5]

Q1
The governing principles in fluid mechanics are the conservation laws for
mass, momentum, and energy. These can be stated either in integral form
when applied to an extended region, or in differential form when applied to a
fluid particle or to an infinitesimal control volume.
(a)
Write in words the conservation law of mass and derive its analytical
expression based on an infinitesimal cubical control volume in a Cartesian
coordinate system, given a generic velocity flow field V=(u,v,w).
[5]
(b)
The lumbar puncture is a common procedure in hospitals where the pressure
within the spinal canal is usually measured and some cerebrospinal fluid
(CSF) is removed either to reduce the pressure or for a sample to be sent for
testing. Write a description of how the lumbar puncture is carried out and list
some conditions that could be diagnosed by testing the CSF.
[5]
(c)
Write down the equation of conservation of linear momentum and describe in
words the meaning of each term appearing into the equation.
[5]
(d)
Simplify the equation of conservation of linear momentum to express the body
pressure as function of the CSF height within the piezometer tube connected
to the spinal canal.
[5]

Added by Briana C.

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