Question

Calculate the depth of a well if the presses at its bottom is 15 times that at a depth of 3m . Atmospheric pressure is 10 m column of water

Answer 1

Depth of a well is $h=185\,m$

Explanation:

The pressure in the liquid column, $P = h \rho g$

'h' denotes the depth of the well.

$P_{atm} + h \rho_{w} g = 15(P_{atm} + 3 \rho_{w}g)$

$= 15P_{atm} + 45 \rho_{w}g$

$h \rho_{w}g  = 15P_{atm} - P_{atm} + 45 \rho_{w}g$

$h \rho_{w}g  = 14P_{atm} + 45 \rho_{w}g$

$h \rho_{w}g  = 14(10 \times\rho_{w}g) + 45 \rho_{w}g$

$h \rho_{w}g  = 140\rho_{w}g + 45 \rho_{w}g$

$h=140+45$

$h=185\,m$

Thus depth of a well is $h=185\,m$.

Answer 2

The depth of a well is 185 m.

Explanation:

Given that,

If the presses at its bottom is 15 times that at a depth of 3m

Depth = 3 m

We need to calculate the depth of a well

Using formula of pressure

$P_{atm}+\rho g h=15(P_{atm}+\rho g\times 3)$

$\rho g h=15P_{atm}-P_{atm}+\rho g\times 45$

$\rho g h=14P_{atm}+\rho g\times 45$

$\rho gh=14\times(\rho g\times 10)+\rho g\times45$

$h=140+45$

$h=185\ m$

Hence, The depth of a well is 185 m.

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Topic : Pressure

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