Water flows through an expansion pipe as illustrated in Figure 1. Q ((A) S 2 m v(s) (B) Figure 1: Schematic of water flowing through an expansion pipe. The velocity along streamline s is given by v = 2t (3 – s) m s¹ where t is in seconds and s is in meters. Assuming viscous effects are negligible, (a) Derive an expression for change in velocity with respect to time. (b) Derive an expression for change in velocity with respect to space. (c) At the instant t = 2 seconds, if the pressure as point A is 20 kPa, determine the pressure gradient, d, needed to produce this flow via application of the Bernoulli equation. (d) What assumption in Bernoulli's equation is clearly violated in this example?

Water flows through an expansion pipe as illustrated in Figure 1. Q ((A) S 2 m v(s) (B) Figure 1: Schematic of water flowing through an expansion pipe. The velocity along streamline s is given by v = 2t (3 – s) m s¹ where t is in seconds and s is in meters. Assuming viscous effects are negligible, (a) Derive an expression for change in velocity with respect to time. (b) Derive an expression for change in velocity with respect to space. (c) At the instant t = 2 seconds, if the pressure as point A is 20 kPa, determine the pressure gradient, d, needed to produce this flow via application of the Bernoulli equation. (d) What assumption in Bernoulli's equation is clearly violated in this example?

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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Concept explainers

Pressurized pipe flow

A 15-kilometer-long pipe with a pipe diameter of one meter transports water at a speed of one meter per second. The pipe has a friction coefficient of 0.005. Calculate the frictional head loss?

Question

Water flows through an expansion pipe as illustrated in Figure 1.
Q
((A)
S
2 m
v(s)
(B)
Figure 1: Schematic of water flowing through an expansion pipe.
The velocity along streamline s is given by v = = 2t(3 s) m s-¹ where t is in seconds
and s is in meters. Assuming viscous effects are negligible,
(a) Derive an expression for change in velocity with respect to time.
(b) Derive an expression for change in velocity with respect to space.
(c) At the instant t = 2 seconds, if the pressure as point A is 20 kPa, determine the
pressure gradient, d, needed to produce this flow via application of the Bernoulli
equation.
(d) What assumption in Bernoulli's equation is clearly violated in this example?

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