Answered: Water flows in a channel with uniform…

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 flows in a channel with uniform curvature R. The channel has height h=ℎ=4mm and width w=200mm (normal to the drawing plane) as shown in Fig Q3. The curved part of the channel has a length of l=115mm in the x-direction. You can assume that the channel height is very small compared to the curvature radius.
Neglect effects of gravity.

Fig Q3: Geometry of curved channel, drawing not to scale. The curvature of the channel is not shown, as too small to be drawn accurately at this scale.

Work to 4 significant digits. Enter all values using base units or their combinations, i.e. m, m/s, Pa, N. Do not use multiples as e.g. mm, kPa.

You can use values with exponents, such as 0.12e3.

=
Water flows in a channel with uniform curvature R. The channel has height h
4 mm and width w=200 mm (normal to the drawing plane) as shown in Fig Q3.
The curved part of the channel has a length of 1=115 mm in the x-direction.
You can assume that the channel height is very small compared to the curvature
radius.
Neglect effects of gravity.
channel
V
X
1
lower wall
h
upper wall
centreline
Fig Q3: Geometry of curved channel, drawing not to scale. The curvature of the
channel is not shown, as too small to be drawn accurately at this scale.
Work to 4 significant digits. Enter all values using base units or their
combinations, i.e. m, m/s, Pa, N. Do not use multiples as e.g. mm, kPa.
You can use values with exponents, such as 0.12e3.

b)
Your team agree that, from experience, the average velocity of
the fluid is v = 48. Assuming that the velocity is uniform
S
across the channel, and neglecting gravitational effects,
determine the curvature R required to generate this force with
this flow velocity.
Use a sign convention that a positive value indicates that the
centre of the radius is above the channel, i.e. the middle of the
channel is bent downwards. A negative radius indicates the
middle of the channel is bent upwards.
The curvature radius R is
m.

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