calculate pressure due to water column of height 100m.(take g=10m s ^-2 and density of water =10^3kg m ^-3
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Answer:-
Given:
Acceleration due to gravity (g) = 10 m/s²
Density of water = 10³ kg/m³
Height = 100 m.
We know that,
Pressure = Force / Area.
- Force = mass * acceleration
- Area = Volume/height.
Force exerted = mass * 10
We know that,
Density = Mass/Volume
Hence,
→ 10³ = Mass / Volume
→ Mass = (10³) * (Volume)
→ Force exerted = 10³ * volume * 10
using a = a¹ and a ^ m * a^n = a^(m + n) we get,
→ Force exerted = 10^(3 + 1) * volume
→ Force = 10⁴ * Volume
And,
Area = Volume/height
- Area = length * breadth
- Volume = length * breadth * height
- → Area = length * breadth * height/height
Hence,
Area occupied = Volume / 100
→ Pressure = (10⁴ * Volume)/(Volume/100)
→ Pressure = (10⁴ * Volume * 100) / Volume
(100 can be written as 10²)
→ Pressure = 10⁴ * 10²
→ Pressure = 10^(4 + 2)
→ Pressure = 10⁶ Pa
→ Pressure = 1 MPa
Therefore, the pressure exerted = 1 MPa.
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