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)​

Answer 1

Given :-

Pressure in water pipe at the ground floor = 1.5 × 10⁵ Pa

Pressure in water pipe on the fifth floor = 2 × 10⁴ Pa

To Find :-

The height of the fifth floor.

Analysis :-

Firstly find the height of the building by substituting the given values in the question.

Then you can easily find the  height of the fifth floor using the formula of pressure exerted accordingly.

Solution :-

We know that,

• p = Pressure
• d = Density
• g = Gravity
• h = Height

Using the formula,

$\underline{\boxed{\sf Pressure=Height \times Density \times Gravity}}$

Given that,

Pressure (p) = 1.5 × 10⁵ Pa

Density (d) = 1000 kg/m³

Gravity (g) = 10 m/s

Substituting their values,

$\sf 1.5 \times 10^5=h \times 1000 \times 10$

$\sf h=\dfrac{1.5 \times 10^5}{10 \times 1000}$

$\sf h=5 \ m$

Therefore, the height of the building is 15 m.

Using the formula,

$\underline{\boxed{\sf Pressure=Height \times Density \times Gravity}}$

Given that,

Pressure (p) = 2 × 10⁵ Pa

Density (d) = 1000 kg/m³

Gravity (g) = 10 m/s

Substituting their values,

$\sf 2 \times 10^4=h \times 1000 \times 10$

$\sf h=\dfrac{2 \times 10^4}{10 \times 1000}$

$\sf h=2 \ m$

Therefore, the height from the tank is 2 m.

According to the question,

Fifth floor is level sixth floor since the ground floor is level one.

$\sf =\dfrac{15}{6} \times 5=12.5 \ m$

Therefore, the height of the fifth floor is 12.5 m.

Answer 2

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

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

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

• 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.