Consider a spiraling line vortex/sink flow in the xy -plane as sketached in Fig. 9-26.The two-dimensional cylindrical velocity components ( u r , u θ ) for this flow field are u r = C / 2 π r , where C and Γ is positive). Verify that this spiraling line vortex/sink flow in the r θ -plane satisfies the two-dimensional incompressible continuity equation. What happens to conservation of mass at the origin? Discuss.
Consider a spiraling line vortex/sink flow in the xy -plane as sketached in Fig. 9-26.The two-dimensional cylindrical velocity components ( u r , u θ ) for this flow field are u r = C / 2 π r , where C and Γ is positive). Verify that this spiraling line vortex/sink flow in the r θ -plane satisfies the two-dimensional incompressible continuity equation. What happens to conservation of mass at the origin? Discuss.
Solution Summary: The author explains the two-dimensional incompressible continuity equation, where the constants are C and Gamma .
Consider a spiraling line vortex/sink flow in the xy-plane as sketached in Fig. 9-26.The two-dimensional cylindrical velocity components
(
u
r
,
u
θ
)
for this flow field are
u
r
=
C
/
2
π
r
, where C and
Γ
is positive). Verify that this spiraling line vortex/sink flow in the
r
θ
-plane satisfies the two-dimensional incompressible continuity equation. What happens to conservation of mass at the origin? Discuss.
A 2-D flow field has velocity components along
X-axis and y-axis given by u = x't and v = -2 xyt
respectively, here, t is time. The equation of
streamline for the given velocity field is :
(а) ху — сonstant
(с) ху' — сonstant
(b) x´y = constant
(d) x + y
constant
In a 2D dimension incompressible flow , if the fluid velocity components are given by u = x-4y , v = -4x then stream function y is given by
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.