Question

Calculate the depth of a well if the pressure at its bottom is 15 times that at a depth of 3m

Answer 1

depth of the well is 185m

Let the depth of the well is h.

pressure at bottom of the well = 15 × pressure at a depth of 3m

⇒Patm + ρgh = 15 × (Patm + ρg × 3)

⇒Patm + ρgh = 15Patm + 45ρg

⇒ρg(h - 45) = 14Patm

we know, Patm = 1.013 × 10^5 N/m² ≈ 10^5 N/m²

ρ = 1000kg/m³ [ density of water ]

g = 10m/s² [ acceleration due to gravity]

so, (h - 45) = 14 × 10^5/(1000 × 10) = 140

⇒h = 185 m

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Answer 2

$\huge\bold\purple{Answer:-}$

The depth of a well is 185 m.