The hydrostatic forces on an aquarium !

Calculus

Manmohan Dash, g6pontiac@gmail.com

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find

(a) The hydrostatic pressure on the bottom of the aquarium,

(b) The hydrostatic force on the bottom, and the hydrostatic force on one end of the aquarium.

Answer;

(a) The hydrostatic pressure on the bottom is obviously ρgh where ρ = 1000kg/m3 and g = 10ms2. Also h = 1m. So P = ρgh = 1000 × 10 × 1 = 10000 Pa. Pa = Pascals; SI unit of pressure.

(b) Now the force on bottom is F = P × A = 10000 × 2 × 1 = 20000 N, where SI unit of force is Newton (N).

For the force on the end of the aquarium we need to take each layer of side wall, as the pressure varies with depth. So F = P × A = ∫10ρ.g.a.xdx where a is the width of the side wall and x is the height of the side wall from bottom (so a × dx = A, area of the strip).

The limit of integration begins from depth of the aquarium to the height of the same, hence (0, 1) Since a = 1, F = 10000 × ∫10xdx = 1/2 × 10000 = 5000 N.

Document generated by eLyXer 1.2.5 (2013-03-10) on 2015-05-31T07:17:26.657000

I am an experimental particle physicist, traveler, teacher, researcher, scientist and communicator of ideas. I am a quarkist and a bit quirky ! Hypothesis non fingo, eppur si muove, dubito cogito ergo sum are things that turn me on ! Researcher in experimental high energy physics (aka elementary particle physics; like “quarks, leptons & mesons and baryons”) … Teacher of Physics (and occasionally chemistry and maths) Blogger (check my website; mdashf.org) ! Love to read read and read but only stuff that interest me. Love to puff away my time in frivolities, just dreaming and may be thinking. Right now desperately trying to streamline myself.

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