The first viscous terms in θ -comonent of the Navier-Stokes eqation (Eq.9-62c) are μ [ 1 r ∂ ∂ r ( r ∂ u θ ∂ r ) − ∂ g r 2 ] . Expand this expression as far as possible using the product rule, yielding three terms. Now combine all there into one term.( Hint: Use the product rule in reverse-some trail and error may be required.)
The first viscous terms in θ -comonent of the Navier-Stokes eqation (Eq.9-62c) are μ [ 1 r ∂ ∂ r ( r ∂ u θ ∂ r ) − ∂ g r 2 ] . Expand this expression as far as possible using the product rule, yielding three terms. Now combine all there into one term.( Hint: Use the product rule in reverse-some trail and error may be required.)
Solution Summary: The author explains the expansion of expression using product rule. Write the expression for the theta component of Navier-Stokes equation.
The first viscous terms in
θ
-comonent of the Navier-Stokes eqation (Eq.9-62c) are
μ
[
1
r
∂
∂
r
(
r
∂
u
θ
∂
r
)
−
∂
g
r
2
]
. Expand this expression as far as possible using the product rule, yielding three terms. Now combine all there into one term.(Hint: Use the product rule in reverse-some trail and error may be required.)
The x-component of the Navier-Stokes equations is given below. Convert it to dimensionless form using
a velocity scale U, a length scale I, and a pressure scale P.
du
at
du du du
+u+v+w. =
ax dy az
1 op μdu du du
+ +
pax² ay ² a=²
pax
An equation for the velocity for a 2D planar converging nozzle is
Uy
u =U1+
w=0
L
Where U is the speed of the flow entering into the nozzle, and L is the length. Determine if these satisfy the continuity
equation. Write the Navier-Stokes equations in x and y directions, simplify them appropriately, and integrate to
determine the pressure distribution P(x.y) in the nozzle. Assume that at x = 0, y = 0, the pressure is a known value, P.
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