Find the pressure at a depth of 10m in water if the atmospheric pressure is 100kPa. [1Pa=1N/m²] [100kPa=105Pa=105N/m²=1 atm.] [Ans: 198 kPa]
Answers
Given conditions ⇒
Depth (d)= 10 m.
Atmospheric Pressure = 100 kPa = 100 × 10³ Pa.
Acceleration due to gravity = 9.8 m/s².
Density of the water = 1000 kg/m³.
Using the Formula,
Pressure = dρg
= 10 × 1000 × 9.8
= 98000 Pa.
= 98 × 10³ Pa.
Total Pressure at the depth of 10 m. = Atmospheric Pressure + Pressure calculated.
= 100 × 10³ + 98 × 10³
= 10³(100 + 98)
= 198 × 10³ Pa.
= 198 kPa. [∵ 10³ = 1 k]
Hence, the Pressure at the depth of 10 m is 198 kPa.
Hope it helps.
198 kPa
Explanation:
Depth of a body in water (h) = 10 m
Density of water (ρ) = 1000 kg/m³
Acceleration due to gravitational force (g) = 9.8 m/s²
Atmospheric pressure (Pₐ) = 100 kPa
Pressure acting on a body in water P = P + Pₐ
P = ρgh + Pₐ
P = ( 1000 × 9.8 × 10 ) + 100 kPa
P = 98 kPa + 100 kPa ( 98000 Pa = 98 kPa )
∴ P = 198 kPa