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A small reservoir has a submerged underwater gate to control its water level. The underwater gate is a two-dimensional rectangular flat-plate, inclined at 450 as shown in Fig. 1, and may be considered weightless. The width of the gate is w and the length is L. The gate is hinged at B and opened by applying a vertical force, T, upwards at A. The vertical distance between the bottom of the gate and the floor of the reservoir is h1, where h1<

A small reservoir has a submerged underwater gate to control its water level. The underwater gate is a two-dimensional rectangular flat-plate, inclined at 450 as shown in Fig. 1, and may be considered weightless. The width of the gate is w and the length is L. The gate is hinged at B and opened by applying a vertical force, T, upwards at A. The vertical distance between the bottom of the gate and the floor of the reservoir is h1, where h1<

Elements Of Electromagnetics
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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A small reservoir has a submerged underwater gate to control its water level. The underwater gate is a
two-dimensional rectangular flat-plate, inclined at 450
as shown in Fig. 1, and may be considered
weightless. The width of the gate is w and the length is L. The gate is hinged at B and opened by applying
a vertical force, T, upwards at A. The vertical distance between the bottom of the gate and the floor of
the reservoir is h1, where h1<<h0. Far downstream, the exiting stream of water is uniform and parallel
and has height h2.
a) Calculate the total hydrostatic force acting on the gate.
b) Calculate the minimum force, T, required to lift the gate.
c) Without detailed calculations, compare the flat plate gate in Fig. 1 with the quarter-circular
cylindrical gate in Fig. 2. Comment on the force required to lift the cylindrical gate.

Question 2: A small reservoir has a submerged underwater gate to control its water level. The underwater gate is a two-dimensional rectangular flat-plate, inclined at 45° as shown in Fig. 1, and may be considered weightless. The width of the gate is w and the length is L. The gate is hinged at B and opened by applying a vertical force, T, upwards at A. The vertical distance between the bottom of the gate and the floor of the reservoir is h, where hị<<ho. Far downstream, the exiting stream of water is uniform and parallel and has height hz. a) Calculate the total hydrostatic force acting on the gate. b) Calculate the minimum force, T, required to lift the gate. c) Without detailed calculations, compare the flat plate gate in Fig. 1 with the quarter-circular cylindrical gate in Fig. 2. Comment on the force required to lift the cylindrical gate. T T Water Water ¼ L ¼ L Hinge Hinge B B ho ho 45° L sin 45° hi hi Figure 1 Figure 2
Transcribed Image Text:Question 2: A small reservoir has a submerged underwater gate to control its water level. The underwater gate is a two-dimensional rectangular flat-plate, inclined at 45° as shown in Fig. 1, and may be considered weightless. The width of the gate is w and the length is L. The gate is hinged at B and opened by applying a vertical force, T, upwards at A. The vertical distance between the bottom of the gate and the floor of the reservoir is h, where hị<<ho. Far downstream, the exiting stream of water is uniform and parallel and has height hz. a) Calculate the total hydrostatic force acting on the gate. b) Calculate the minimum force, T, required to lift the gate. c) Without detailed calculations, compare the flat plate gate in Fig. 1 with the quarter-circular cylindrical gate in Fig. 2. Comment on the force required to lift the cylindrical gate. T T Water Water ¼ L ¼ L Hinge Hinge B B ho ho 45° L sin 45° hi hi Figure 1 Figure 2
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