Lecture F13 Mud: Bernoulli Equation
(25 respondents)
1.
How is
ρu du/dx
=
1
2
ρ d
(
u
2
)
/dx
?
(2 students)
You can see this easily just by differentiating
d
(
u
2
)
/dx
via the product rule.
2.
How is
ρu du
=
1
2
ρ d
(
u
2
)
?
(2 students)
Take the differential
d
(
u
2
) using the product rule. This is essentially the same operation
as in mud 1 above.
3.
How did you go from
1
2
ρ d
(
u
2
)
/dx
+
dp/dx
= 0
to
1
2
ρ u
2
+
p
=
C
?
(1 student)
Via an indefinite integration in
x
:
integraldisplay parenleftbigg
1
2
ρ d
(
u
2
)
/dx
+
dp/dx
= 0
parenrightbigg
dx
4.
How did you know you can multiply
x
momentum by
dx
?
(1 student)
You can always multiply equations by anything you want, whether it’s useful or not
to do so. Bernoulli in the 1700’s figured out that multiplying by
dx
actually gets you
somewhere.
5.
What form of
vector
V
should you use in Bernoulli?
∇
φ
?
(1 student)
In aerodynamic flows, the velocity used in Bernoulli is usually defined via
φ
(
x, y, z
).
There are exceptions, however, such as when a pitot probe is used inside a boundary
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 MarkDrela
 Derivative, Product Rule, Aerodynamics, Airfoil, Bernoulli's principle

Click to edit the document details