Read before you solve · 3 min

Read Draining Tanks: Combine Geometry with Torricelli

This short read prepares one exact NSEP pattern: emptying a hemispherical tank. Identify the physical condition before calculating.

NSEP · Fluid Mechanics · 1 linked question · 100% coverage

Know this first

Emptying a Hemispherical Tank is the central idea in this question pattern. Identify the condition in the stem before applying the method below.

Study deeper: NCERT Physics · Fluid Mechanics

Start with the physical model

Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.

At water depth y above the bottom of a hemisphere, the horizontal cross-sectional area is A(y)=π[2Ry-y2].

Torricelli gives efflux speed

v = sqrt(2gy), so A(y)dy = -a sqrt(2gy) dt

Integrating from initial

h = R/2 to 0 gives t = (π/a√(2g))∫0 R/2(2Ry-y2)y-1/2dy = 17πR2sqrt(R/g)/(60a)

Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.

OlympIQ trap

A hemispherical tank's cross-sectional area varies with water height; do not use a cylindrical-tank formula.

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