Question

The pressure in water pipe at the ground floor of a building is 1.5 x 105 Pa, whereas the pressure on fifth floor is 2 x 104 Pa. Calculate the height of the fifth floor. (Take g = 10 ms-2)

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Answer 1

The pressure in water pipe at the ground floor of a building is 1.5 x 105 Pa, whereas the pressure on fifth floor is 2 x 104 Pa. Calculate the height of the fifth floor. (Take g = 10 ms-2)

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Answer 2

$\Large\bf{\color{indigo}GiVeN,}$

• The pressure in water pipe at the ground floor of a building is 1.5 × 10⁵ La

$\longrightarrow\:\:\bf\blue{P_{o}\:=\:1.5\times{10^5}\:Pa}$

• The pressure in water pipe on fifth floor is 2 × 10⁴ Pa.

$\longrightarrow\:\:\bf\red{P_{(5th\:floor)}\:=\:2\times{10^4}\:Pa}$

$\bf\purple{Let,}$

• Height of the 5th floor is 'h' m.

☆ Change in pressure due to height is,

$\longmapsto\:\:\bf{\triangle{P}\:=\:P_{o}\:-\:P_{(5th\:floor)}\:}$

$\longmapsto\:\:\bf{\triangle{P}\:=\:15\times{10^5}\:-\:2\times{10^4}\:}$

$\longmapsto\:\:\bf{\triangle{P}\:=\:15\times{10^4}\:-\:2\times{10^4}\:}$

$\longmapsto\:\:\bf\orange{\triangle{P}\:=\:13\times{10^4}\:Pa\:}$

$\bf\pink{We\:know\:that,}$

$\red\bigstar\:\:{\green{\boxed{\bf{\color{peru}\triangle{P}\:=\:{\rho}_{w}\:g\:h\:}}}}$

$\bf\green{Where,}$

• $\bf{\rho_w}$ is the density of water, i.e 10³ kg/m³.

• g is gravitational constant, i.e. 10 m/s².

• h is the height of the 5th floor.

$:\implies\:\:\bf{13\times{10^4}\:=\:\rho_w\:g\:h\:}$

$:\implies\:\:\bf{h\:=\:\dfrac{13\times{10^4}}{\rho_w\:g}\:}$

$:\implies\:\:\bf{h\:=\:\dfrac{13\times{10^4}}{10^3\times{10}}\:}$

$:\implies\:\:\bf{h\:=\:\dfrac{13\times{10^4}}{10^4}\:}$

$:\implies\:\:\bf\blue{h\:=\:13\:m\:}$

$\Large\bold\therefore$ The height of the 5th floor is 13 m.