EGM 6812 Fluid Mechanics 1  Fall 2010
10/25/10, 8
th
Homework
1/3
1.
Starting with the Cartesian form of the NS equation, derive Bernoulli’s equation for
incompressible, inviscid, and irrotational flow.
Please state all assumptions and show all
steps.
2.
Starting with the integral form of the energy equation, derive Bernoulli’s equation for a
conservative fluid system.
Please state all assumptions and show all steps.
3.
Consider a static pressure tap drilled into the surface of a wind tunnel model under two
different scenarios shown below.
In case (a), a burr is formed prior to the hole deflecting the
streamlines upward over the hole.
In case (b), a burr is formed after the hole.
Which
situation will result in a measurement error to due a pressure increase and which one will
result in a decrease?
Explain your answer both mathematically and physically.
4.
Consider the inviscid flow of water (assume a constant density
) over the surfaces shown
below.
For each case, the depth
h
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 Fall '09
 RENWEIMEI
 Fluid Dynamics, Fluid Mechanics, irrotational flow, Pitot tube, static port

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