What is the pressure at the bottom of a river (12 m deep) if the air pressure over the river is 98.23 kPa? The density of the river water is 988 kg/m3.
To find the pressure at the bottom of a river, we can use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at a certain depth due to the weight of the fluid above it.
The formula to calculate hydrostatic pressure is as follows:
P = ρ * g * h
where:
P is the hydrostatic pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth from the surface.
Given the following values:
ρ (density of river water) = 988 kg/m³
g (acceleration due to gravity) = 9.8 m/s²
h (depth from the surface) = 12 m
We can substitute these values into the formula to find the pressure at the bottom of the river.
P = 988 kg/m³ * 9.8 m/s² * 12 m
First, multiply 988 kg/m³ by 9.8 m/s²:
988 kg/m³ * 9.8 m/s² = 9682.4 N/m² or Pascal (Pa)
Then, multiply the result by 12 m:
9682.4 N/m² * 12 m = 116188.8 N/m² or Pascal (Pa)
Now, we need to convert the pressure from Pascal to kilopascals (kPa). Since 1 kPa = 1000 Pa, we divide the value by 1000:
116188.8 N/m² / 1000 = 116.1888 kPa
Therefore, the pressure at the bottom of the river is approximately 116.19 kPa.