Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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Consider the incompressible Newtonian pipe flow (Fig. 6). Assume the flow is essentially
axial, vz ≠ 0 but vr = v = 0 and ∂/∂ = 0. The flow is fully developed and steady in a horizontal pipe with
the constant pressure gradient. Apply the Navier-Stokes equations and:
Transcribed Image Text:### Problem 6: Incompressible Newtonian Pipe Flow
Consider the incompressible Newtonian pipe flow (Fig. 6). Assume the flow is essentially axial, \( v_z \neq 0 \) but \( v_r = v_\theta = 0 \) and \(\partial/\partial \theta = 0\). The flow is fully developed and steady in a horizontal pipe with the constant pressure gradient. Apply the Navier-Stokes equations and:
a) Develop simplified governing equations (continuity and momentum) for this flow;
b) Apply the boundary conditions and determine the velocity profile; and
c) Develop expressions for the flow rate and mean velocity from the velocity profile.
### Diagram Explanation
**Fig. 6: Flow in Circular Pipe**
The diagram illustrates a circular pipe with flow moving in the axial direction. The arrows indicate the direction and relative magnitude of the velocity, \( v_z \), which varies across the radius of the pipe. The centerline indicates the direction of maximum velocity, while the velocity decreases towards the pipe walls. The pipe is depicted in cross-section, showing the symmetrical nature of the flow profile.
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