1. Start from the following equations from class notes (treat as given) The shear stress in pipe flow T=-μ= du dr The fluid velocity in the pipe u = APP² [1-³]. 16μL Derive clearly the following results: (a) The "1 CAL where L is the I

Elements Of Electromagnetics
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1.
Start from the following equations from class notes (treat as given):
The shear stress in pipe flow T = -μ- dr
du
16 [1-(-)²),
AP D²
16μL
The fluid velocity in the pipe u =
Derive clearly the following results:
(a) The shear stress on the wall of the pipe, Tw.
(b) The average velocity in the pipe flow, ū.
(c) The Darcy friction factor, defined by f
where L is the length of the pipe.
8 tw
pū²
(d) Express the result of (c) in terms of the Reynolds number, Re.
(e) Find an expression for the head loss due to shear stress at the wall, AH₁, in terms of
f,u, D and L.
(f) What are the main assumptions in the fluid flow, in order to analyse the flow in this
way?
Transcribed Image Text:1. Start from the following equations from class notes (treat as given): The shear stress in pipe flow T = -μ- dr du 16 [1-(-)²), AP D² 16μL The fluid velocity in the pipe u = Derive clearly the following results: (a) The shear stress on the wall of the pipe, Tw. (b) The average velocity in the pipe flow, ū. (c) The Darcy friction factor, defined by f where L is the length of the pipe. 8 tw pū² (d) Express the result of (c) in terms of the Reynolds number, Re. (e) Find an expression for the head loss due to shear stress at the wall, AH₁, in terms of f,u, D and L. (f) What are the main assumptions in the fluid flow, in order to analyse the flow in this way?
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