Fully laminar flow in cylindrical pipe Consider the steady, viscous flow of Newtonian (dynamic viscosity), incompressible(density ρ ) fluid through a pipe with a circular cross-section (radius R) under the constantpressure gradient in the x-directionwhere x1 and x2 are two arbitrary locations along the x-axis, and P1 and P2 are the pressures at those two locations (note that we adopt a modified cylindrical coordinate system here with x instead of z for the axial component, namely, (r, , x)). Coordinates of fluid velocity in the cylindrical coordinates are (ur , u, u). - Show that the velocity field inside the pipe is (0, 0, u) and (photo)- Show that the flow discharge Q is (photo) -Show that the velocity field inside the pipe is (0, 0, u) and1 dP4μ dxShow that the flow discharge Q isQ-(²-R²)JPaxTR dP8μ dxPipe wallFluid: p. pRP₂-P₁X2-X1X₂ Fully laminar flow in cylindrical pipeConsider the steady, viscous flow of Newtonian (dynamic viscosity μ), incompressible(density p) fluid through a pipe with a circular cross-section (radius R) under the constantpressure gradient in the x-directionApplied pressure gradient:apaxP₂ - P₁X₂ - X₁= constantwhere X₁ and X₂ are two arbitrary locations along the x-axis, and P₁ and P₂ are the pressuresat those two locations (note that we adopt a modified cylindrical coordinate system here withx instead of z for the axial component, namely, (r, 0, x)). Coordinates of fluid velocity in thecylindrical coordinates are (ur, ue, u).

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Answered: Show that the velocity field inside the…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Fully laminar flow in cylindrical pipe

Consider the steady, viscous flow of Newtonian (dynamic viscosity), incompressible
(density ρ ) fluid through a pipe with a circular cross-section (radius R) under the constant
pressure gradient in the x-direction
where x1 and x2 are two arbitrary locations along the x-axis, and P1 and P2 are the pressures
at those two locations (note that we adopt a modified cylindrical coordinate system here with
x instead of z for the axial component, namely, (r, , x)). Coordinates of fluid velocity in the
cylindrical coordinates are (ur , u, u).

- Show that the velocity field inside the pipe is (0, 0, u) and (photo)
- Show that the flow discharge Q is (photo)

-
Show that the velocity field inside the pipe is (0, 0, u) and
1 dP
4μ dx
Show that the flow discharge Q is
Q
-(²-R²)
JP
ax
TR dP
8μ dx
Pipe wall
Fluid: p. p
R
P₂-P₁
X2-X1
X₂

Fully laminar flow in cylindrical pipe
Consider the steady, viscous flow of Newtonian (dynamic viscosity μ), incompressible
(density p) fluid through a pipe with a circular cross-section (radius R) under the constant
pressure gradient in the x-direction
Applied pressure gradient:
ap
ax
P₂ - P₁
X₂ - X₁
= constant
where X₁ and X₂ are two arbitrary locations along the x-axis, and P₁ and P₂ are the pressures
at those two locations (note that we adopt a modified cylindrical coordinate system here with
x instead of z for the axial component, namely, (r, 0, x)). Coordinates of fluid velocity in the
cylindrical coordinates are (ur, ue, u).

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