5. Fig. 1 shows a gate of length l and mass m pivoted on its top edge, A, at the water level of a reservoir. The gate is free to swing in an arc and is in equilibrium in the condition shown. There is no leakage at point B and both friction and air pressure can be neglected. a. By considering the pressure acting on an infintessimal element of the gate, show that the anticlockwise moment, M, due to the water, about A, is given by: 1 M =zpgbl° cos 0 where b is the width of the gate (into the page) and p is the density of the water. b. Calculate 0 given that l = 1 m and the mass of the gate is 1000 kg per unit width. PA b I cos0 Figure 1

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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5. Fig. 1 shows a gate of length l and mass m pivoted on its top edge, A, at the water level
of a reservoir. The gate is free to swing in an arc and is in equilibrium in the condition
shown. There is no leakage at point B and both friction and air pressure can be
neglected.
a. By considering the pressure acting on an infintessimal element of the gate, show
that the anticlockwise moment, M, due to the water, about A, is given by:
1
M =
3Pgbl3
where b is the width of the gate (into the page) and p is the density of the water.
cos 8
b. Calculate 0 given that l =1 m and the mass of the gate is 1000 kg per unit width.
%3D
PA
b
I cose
Figure 1
Transcribed Image Text:5. Fig. 1 shows a gate of length l and mass m pivoted on its top edge, A, at the water level of a reservoir. The gate is free to swing in an arc and is in equilibrium in the condition shown. There is no leakage at point B and both friction and air pressure can be neglected. a. By considering the pressure acting on an infintessimal element of the gate, show that the anticlockwise moment, M, due to the water, about A, is given by: 1 M = 3Pgbl3 where b is the width of the gate (into the page) and p is the density of the water. cos 8 b. Calculate 0 given that l =1 m and the mass of the gate is 1000 kg per unit width. %3D PA b I cose Figure 1
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