Recall that the transverse velocity for Poiseuille flow is Ap u(r) = 4µL + cị Inr+ c2, 0 < r < R, where Ap/L is the (constant) pressure gradient, u is the dynamic viscosity, and L is the length of the tube. Since the solution can't blow up at r = 0, c¡ = 0, and c, is determined by the no-slip condition u(R) = 0. Integrating the resulting solution over the cross- section of the tube gives the flux TR* Ap Qo 8µ L Now imagine that the tube has a central catheter so that R

Recall that the transverse velocity for Poiseuille flow is Ap u(r) = 4µL + cị Inr+ c2, 0 < r < R, where Ap/L is the (constant) pressure gradient, u is the dynamic viscosity, and L is the length of the tube. Since the solution can't blow up at r = 0, c¡ = 0, and c, is determined by the no-slip condition u(R) = 0. Integrating the resulting solution over the cross- section of the tube gives the flux TR* Ap Qo 8µ L Now imagine that the tube has a central catheter so that R

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

Recall that the transverse velocity for Poiseuille flow is
Др
4µL
u(r) =
P² + c1
Inr + c2,
0 < r < R,
where Ap/L is the (constant) pressure gradient, u is the dynamic viscosity, and Lis the length of the tube. Since the solution can't
blow up at r = 0, c1 = 0, and c2 is determined by the no-slip condition u(R) = 0. Integrating the resulting solution over the cross-
section of the tube gives the flux
TRA Ap
Qo
8µ L
1
R< r < R. Use the solution for u above and apply no-slip conditions at
3
Now imagine that the tube has a central catheter so that
1
R and r = R to compute the flux Q for the catheterized tube.
3
r =

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A smooth square cylinder is put in 15 °C flowing water. The flow direction is perpendicular to the long axis of the cylinder (parallel to the square section). The edge length of the square is s=2.0m. The long axis length is L=5.0m. The flow velocity is v=0.046 m/s. The density of water is ρ=1000kg/m3. T he dynamic viscosity is η=1.15×10-3kg/m·s. (3) Calculate the drag force FD_________N (2 decimal places)
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