1. an aquarium 5 ft long, 2 ft wide, and 3 ft deep is full of water. find (a) the hydrostatic pressure on the bottom of the aquarium, (b) the hydrostatic force on the bottom, and (c) the hydrostatic force on one end of the aquarium

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19-12-2022
Physics

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1. an aquarium 5 ft long, 2 ft wide, and 3 ft deep is full of water. find (a) the hydrostatic pressure on the bottom of the aquarium, (b) the hydrostatic force on the bottom, and (c) the hydrostatic force on one end of the aquarium

Answer :

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kjuli1766 kjuli1766 · Answer 1 · 2022-12-21T22:36:22-05:00

(a).the hydrostatic pressure on the bottom of the aquarium is 312.5 lb/ft²

(b) the hydrostatic force on the bottom is 4681.5 lb

(c) the hydrostatic force on one end of the aquarium is 2343.75 lb.

Calculation :

Given , long = 5 ft

wide = 3 ft

deep = 5 ft

a). hydrostatic pressure

p= 5.(depth)

= 62.5 x 5

= 312.5 lb/ft²

b). hydrostatic force

F = pressure x area

= (312.5) x 15

= 4681.5 lb

c). Let a strip of Δx at the distance x.

width of strip = 3 ft

area of strip = 3Δx

pressure of strip = 62.5(5 - x)

force = 62.5 (5 - x) (3Δx)

the total force,

F = [tex]\int\limits^0_5 {62.5*3*(5 - x)} \, dx[/tex]

= 187.3[ 5x - x²/2 ]⁵₀

= 187.3[ 5x - 25/2 ]⁵₀

= 187.3 x (25/2)

= 2343.75 lb

Hydrostatic pressure is a branch of fluid mechanics that studies the equilibrium state of floating and submerged bodies. It involves the study of conditions in which the fluid is at rest in stable equilibrium, in contrast to fluid mechanics, which is the study of fluids in motion.

Hydrostatic pressure is a subcategory of hydrostatics and is the study of all fluids, both compressible and incompressible at rest.

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