Answer :
To calculate the pressure exerted by water at a given height, we can use the hydrostatic pressure formula, which relates the pressure to the density of the fluid, the height of the fluid column, and the acceleration due to gravity.
The formula for hydrostatic pressure is:
[tex]\[ P = \rho \cdot g \cdot h \][/tex]
where:
- [tex]\( P \)[/tex] is the pressure,
- [tex]\( \rho \)[/tex] (rho) is the density of the fluid (water in this case),
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height of the fluid column.
Given:
- The density of water, [tex]\( \rho = 1000 \, \text{kg/m}^3 \)[/tex] (common value for the density of water),
- The height, [tex]\( h = 2 \, \text{m} \)[/tex],
- The acceleration due to gravity, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].
We substitute these values into the formula:
[tex]\[ P = 1000 \, \text{kg/m}^3 \cdot 9.8 \, \text{m/s}^2 \cdot 2 \, \text{m} \][/tex]
Now, we multiply these values together to find the pressure:
[tex]\[ P = 1000 \cdot 9.8 \cdot 2 \][/tex]
[tex]\[ P = 19600 \][/tex]
Therefore, the pressure exerted by the water at a height of 2 meters is:
[tex]\[ \boxed{19600 \, \text{Pa}} \][/tex]
where Pa (Pascals) is the unit of pressure.
The formula for hydrostatic pressure is:
[tex]\[ P = \rho \cdot g \cdot h \][/tex]
where:
- [tex]\( P \)[/tex] is the pressure,
- [tex]\( \rho \)[/tex] (rho) is the density of the fluid (water in this case),
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height of the fluid column.
Given:
- The density of water, [tex]\( \rho = 1000 \, \text{kg/m}^3 \)[/tex] (common value for the density of water),
- The height, [tex]\( h = 2 \, \text{m} \)[/tex],
- The acceleration due to gravity, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].
We substitute these values into the formula:
[tex]\[ P = 1000 \, \text{kg/m}^3 \cdot 9.8 \, \text{m/s}^2 \cdot 2 \, \text{m} \][/tex]
Now, we multiply these values together to find the pressure:
[tex]\[ P = 1000 \cdot 9.8 \cdot 2 \][/tex]
[tex]\[ P = 19600 \][/tex]
Therefore, the pressure exerted by the water at a height of 2 meters is:
[tex]\[ \boxed{19600 \, \text{Pa}} \][/tex]
where Pa (Pascals) is the unit of pressure.
