Question 4 This question shows an application of multiple integrals in engineering and some self-learning should be expected. In an underwater sea aquarium, two acrylic glass panels in the shapes shown below are to be installed for visitors to view the marine life. Figure Q4 shows the front view of the aquarium: the left drawing is of a rectangular vertical panel and the right drawing is of a semi-circular vertical panel. h W H R J (All dimensions are in meters.) Figure Q4 In order to determine the thickness of the panels and their attachment method to the surrounding wall, the net force caused by the hydrostatic water pressure must be determined. Under a liquid of density p, the hydrostatic pressure is P = pgh (Pa) where h is the depth from the free surface of the liquid. (a) With a sketch of the region of integration (axes must be clearly labelled), set up a double integral that gives the net hydrostatic force acting on the rectangular panel. Hence, evaluate the net hydrostatic force as a function of p, g, H and W.
Question 4 This question shows an application of multiple integrals in engineering and some self-learning should be expected. In an underwater sea aquarium, two acrylic glass panels in the shapes shown below are to be installed for visitors to view the marine life. Figure Q4 shows the front view of the aquarium: the left drawing is of a rectangular vertical panel and the right drawing is of a semi-circular vertical panel. h W H R J (All dimensions are in meters.) Figure Q4 In order to determine the thickness of the panels and their attachment method to the surrounding wall, the net force caused by the hydrostatic water pressure must be determined. Under a liquid of density p, the hydrostatic pressure is P = pgh (Pa) where h is the depth from the free surface of the liquid. (a) With a sketch of the region of integration (axes must be clearly labelled), set up a double integral that gives the net hydrostatic force acting on the rectangular panel. Hence, evaluate the net hydrostatic force as a function of p, g, H and W.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q4 a
Needed with Sketch
Transcribed Image Text:Question 4
This question shows an application of multiple integrals in engineering and some self-learning
should be expected.
In an underwater sea aquarium, two acrylic glass panels in the shapes shown below are to be
installed for visitors to view the marine life. Figure Q4 shows the front view of the aquarium:
the left drawing is of a rectangular vertical panel and the right drawing is of a semi-circular
vertical panel.
h
W
H
(All dimensions are in meters.)
Figure Q4
R
In order to determine the thickness of the panels and their attachment method to the surrounding
wall, the net force caused by the hydrostatic water pressure must be determined. Under a liquid
of density p, the hydrostatic pressure is
P = pgh (Pa)
where h is the depth from the free surface of the liquid.
(a)
With a sketch of the region of integration (axes must be clearly labelled), set up a double
integral that gives the net hydrostatic force acting on the rectangular panel. Hence,
evaluate the net hydrostatic force as a function of p, g, H and W.
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