Consider steady incompressible flow in the entrance region of a horizontal circular tube of radius, R, and length L. The direction of flow is along the x coordinate. The flow at the inlet (location 1, x = is uniform, ui = flow for which the velocity profile, u2 = 0) Uo. The flow at a downstream location (location 2, x = L) is fully developed laminar Umax (1 – r2/R²). The pressures at the two locations are p1 and P2, and the fluid density is p. a. Using basic equations (5.5) and (5.22), determine the total friction force exerted by the tube on the fluid (magnitude and direction) as a function of known quantities, P1, P2, P, Uo, R, L. b. Evaluate the total friction force for the case of air at 15°C, R = 12.5 mm, L = 2.6 m, U, = 0.87 m/s. The measured pressure drop is Ap = p1 – P2 = 1.92 N/m². Verify that the flow is laminar. Is it reasonable to expect fully developed flow at L= 2.6 m? Explain/justify.
Consider steady incompressible flow in the entrance region of a horizontal circular tube of radius, R, and length L. The direction of flow is along the x coordinate. The flow at the inlet (location 1, x = is uniform, ui = flow for which the velocity profile, u2 = 0) Uo. The flow at a downstream location (location 2, x = L) is fully developed laminar Umax (1 – r2/R²). The pressures at the two locations are p1 and P2, and the fluid density is p. a. Using basic equations (5.5) and (5.22), determine the total friction force exerted by the tube on the fluid (magnitude and direction) as a function of known quantities, P1, P2, P, Uo, R, L. b. Evaluate the total friction force for the case of air at 15°C, R = 12.5 mm, L = 2.6 m, U, = 0.87 m/s. The measured pressure drop is Ap = p1 – P2 = 1.92 N/m². Verify that the flow is laminar. Is it reasonable to expect fully developed flow at L= 2.6 m? Explain/justify.
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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Question
Answer the following question using the format given.

Transcribed Image Text:2. The following is the standard format for organizing and presenting the solution to a fluid mechanics
problem. Use this (or similar clear, organized, logical procedure) in your homework.
(a) Problem Description - include the following:
• Given information and basic description.
• Schematic of problem/geometry. Clearly indicate system/control volume considered,
coordinate system, any other relevant information.
• What is to be determined.
(b) List of Assumptions - list all appropriate simplifying assumptions.
(c) Basic Equations - general form of relevant fundamental laws, equations, definitions.
(d) Analysis
• clearly describe procedure to apply/manipulate/reduce equations to give solution.
• reference all tables and charts needed for physical properties and other data.
• substitute numerical values into final equations. be sure to specify all units
and unit conversions.
• keep significant figures consistent with given data.
• check solution - correct sign, reasonable numerical values?
• clearly indicate final answer(s) with underline or box.
(e) Discussion of Solution - as needed (what you learned, key aspects of solution, etc).

Transcribed Image Text:Consider steady incompressible flow in the entrance region of a horizontal circular tube of radius, R,
and length L. The direction of flow is along the x coordinate. The flow at the inlet (location 1, x =
is uniform, ui =
flow for which the velocity profile, u2 =
and p2, and the fluid density is p.
= 0)
Uo. The flow at a downstream location (location 2, x = L) is fully developed laminar
Umaz (1 – r2/R²). The pressures at the two locations are p1
a. Using basic equations (5.5) and (5.22), determine the total friction force exerted by the tube on
the fluid (magnitude and direction) as a function of known quantities, p1, P2, P, U,, R, L.
b. Evaluate the total friction force for the case of air at 15°C, R =
m/s. The measured pressure drop is Ap = Pi – P2
Is it reasonable to expect fully developed flow at L = 2.6 m? Explain/justify.
12.5 mm, L
2.6
m,
= 0.87
1.92 N/m2. Verify that the flow is laminar.
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