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.
P = (rho)*g*(depth) + Po
rho is the density of the water
depth = 12 m
g = 9.8 m/s^2
Po = 98.23*10^3 N/m^2
Solve for P
To find the pressure at the bottom of the river, you can use the hydrostatic pressure equation:
P = P0 + ρgh
where:
P is the pressure at the bottom of the river,
P0 is the air pressure over the river,
ρ is the density of the river water, and
h is the depth of the river.
First, convert the given air pressure to pascals (Pa):
P0 = 98.23 kPa × 1000 = 98,230 Pa
Next, substitute the given values into the equation:
P = 98,230 Pa + (988 kg/m^3) × 9.8 m/s^2 × 12 m
Now, calculate the pressure at the bottom of the river:
P = 98,230 Pa + 115,065.6 Pa
P ≈ 213,296 Pa
Therefore, the pressure at the bottom of the river is approximately 213,296 Pa.
To find the pressure at the bottom of a river, we need to consider two factors: the depth of the river and the density of the water.
The pressure at a certain depth in a fluid can be calculated using the formula:
Pressure = Pressure at the surface + (Density of the fluid × Acceleration due to gravity × Depth)
Let's calculate the pressure at the bottom of the river using the given values:
First, we need to convert the depth from meters to pascals. Since 1 Pascal is equal to the pressure exerted by a force of 1 Newton on an area of 1 square meter, we can use the conversion factor:
1 m = 1,000,000 Pa
So, the depth of the river becomes:
Depth = 12 m × 1,000,000 Pa/m = 12,000,000 Pa
Next, we can substitute the given values into the formula:
Pressure at the bottom = 98.23 kPa + (988 kg/m^3 × 9.8 m/s^2 × 12,000,000 Pa)
Now let's calculate the pressure at the bottom of the river:
Pressure at the bottom = 98.23 kPa + (988 kg/m^3 × 9.8 m/s^2 × 12,000,000 Pa)
Pressure at the bottom = 98.23 kPa + 114,422,400 Pa
Adding these two values gives us:
Pressure at the bottom ≈ 114,422,498.23 Pa
Therefore, the pressure at the bottom of the river is approximately 114,422,498.23 Pa.