Water at 40 °C (? = 992.3 ?? ??? ? = 0.664 × 10−6 ?2/?) flows at a velocity of 2 m/s through a pipe with a diameter of 20 mm and a friction factor of f = 0.004. The water enters the pipe at point A (Figure Q2) into a bath shower mixer unit out of which, the water can exit through the spout via a gate valve (Figure Q2a) or through the showerhead (Figure Q2b). a. If the water exits through the spout (Figure Q2a) via a fully opened gate valve at B, with a diameter of 12 mm, determine the water pressure at point A. The minor loss coefficient is Kspout = 0.6 for the spout at B. Account for the minor loss in the elbow, the tee, and the gate valve. The gate valve at E is closed. b. If the water emerges through the showerhead (Figure Q2b, point C) that consists of 100 identical holes, each with a diameter of 1.5 mm. Determine the pressure of the water at A if the minor loss coefficient is Kshowerhead = 0.45 for the showerhead. The gate valve at B is closed. Account for the minor loss in the three elbows, the fully opened gate valve at E, and the tee. M1 = 1.330m M2 = 2.330m M3 = 1.015m Table of Loss Coeffcients Loss Coeffcients KL Gate Valve - Fully Open 0.19 90° Bend 0.9 45° Bend 0.4 Tee for Valve along Branch 1.8

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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Water at 40 °C (? = 992.3 ?? ??? ? = 0.664 × 10⁻⁶ ?²/?) flows at a velocity of 2 m/s through a pipe with a diameter of 20 mm and a friction factor of f = 0.004. The water enters the pipe at point A (Figure Q2) into a bath shower mixer unit out of which, the water can exit through the spout via a gate valve (Figure Q2a) or through the showerhead (Figure Q2b).

a. If the water exits through the spout (Figure Q2a) via a fully opened gate valve at B, with a diameter of 12 mm, determine the water pressure at point A. The minor loss coefficient is K_spout = 0.6 for the spout at B. Account for the minor loss in the elbow, the tee, and the gate valve. The gate valve at E is closed.

b. If the water emerges through the showerhead (Figure Q2b, point C) that consists of 100 identical holes, each with a diameter of 1.5 mm. Determine the pressure of the water at A if the minor loss coefficient is K_showerhead = 0.45 for the showerhead. The gate valve at B is closed. Account for the minor loss in the three elbows, the fully opened gate valve at E, and the tee.

M₁ = 1.330m

M₂ = 2.330m

M₃ = 1.015m

Table of Loss Coeffcients

Loss Coeffcients	K_L
Gate Valve - Fully Open	0.19
90° Bend	0.9
45° Bend	0.4
Tee for Valve along Branch	1.8

a
0.15 m
M₂
D
0.08 m
M₁
A
M3
E
b
0.15 m
M₂
D
0.08 m
M₁
A
M3
HE
FB
Figure Q2. Bath shower mixer unit with water entering the system at point A and
exiting through (a) spout located at point B and (b) shower head located at point C.

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