Calculate the pressure at a point 5 m below the free water surface in a liquid that has a variable density given by equation o =(350+Ay)kg/m3, where A = 8 kg/m4 and y is the distance in meters measured from the free surface.
what is the pressure at apoint 10 m below the free surface in fluid that has with solution variable density in kg/m3 given by p=45+ah, in which a=12 kg/m4 and h is the distance measured from the free surface with solution
To calculate the pressure at a point below the free water surface, we can use the hydrostatic pressure equation:
P = P₀ + ρgh
where:
P = pressure at the given point
P₀ = pressure at the free water surface (usually atmospheric pressure)
ρ = density of the liquid
g = acceleration due to gravity
h = depth or distance from the free surface
Given:
Density equation: ρ = (350 + Ay) kg/m³
A = 8 kg/m^4
h = 5 m
First, we need to find the density at the point 5 m below the free surface.
Plug in the value of y = 5 into the density equation:
ρ = (350 + A(5))
ρ = (350 + 8(5))
ρ = (350 + 40)
ρ = 390 kg/m³
Now, we can substitute the values into the hydrostatic pressure equation:
P = P₀ + ρgh
Assuming the pressure at the free water surface is atmospheric pressure (usually 101,325 Pa or 1 atm), we can use this value for P₀.
P = 101,325 Pa + 390 kg/m³ × 9.8 m/s² × 5 m
Simplifying the equation:
P ≈ 101,325 Pa + 19,110 Pa
Therefore, the pressure at a point 5 m below the free water surface is approximately:
P ≈ 120,435 Pa
To calculate the pressure at a point 5 m below the free water surface in a liquid with a variable density given by the equation o = (350 + Ay) kg/m^3, where A = 8 kg/m^4 and y is the distance in meters measured from the free surface, you can use the concept of hydrostatic pressure.
Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It can be calculated using the formula:
P = ρgh,
Where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth or distance below the free surface.
In this case, the density is variable and given by the equation o = (350 + Ay) kg/m^3, where A = 8 kg/m^4 and y is the depth or distance below the free surface.
Let's determine the steps to calculate the pressure at a point 5 m below the free water surface.
Step 1: Convert the given equation for density into the standard form of density.
The given equation for density is o = (350 + Ay) kg/m^3.
To convert it to the standard form, we can expand the equation:
o = 350 kg/m^3 + A(y) kg/m^3
Substituting the value of A = 8 kg/m^4:
o = 350 kg/m^3 + 8(y) kg/m^4
Step 2: Substitute the value of density (ρ) into the hydrostatic pressure equation.
P = ρgh
Substituting the value of density (ρ) as (350 + 8y) kg/m^3, and the value of g as the standard acceleration due to gravity (9.8 m/s^2), we get:
P = (350 + 8y) kg/m^3 × 9.8 m/s^2 × (depth, h)
Step 3: Calculate the pressure at a point 5 m below the free water surface.
To find the pressure at a depth of 5 m below the free surface, substitute the value of the depth (h) as 5 m:
P = (350 + 8(5)) kg/m^3 × 9.8 m/s^2
Simplifying the equation:
P = (350 + 40) kg/m^3 × 9.8 m/s^2
P = 390 kg/m^3 × 9.8 m/s^2
P = 3822 N/m^2 or Pascal (Pa)
The pressure at a point 5 m below the free water surface in the given liquid is 3822 Pa.