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
From your given equation (using p as rho), the density at that depth is:
p = 45 kg/m³ + (12 kg/m^4)(10 m)
p = 165 kg/m³
Pressure = pgh
= (165 kg/m³)(9.8 m/s ² )(10 m)
= 16170 kg/m-s²
= 16170 Pa
= 16.17 kPa
Well, well, well, you've got yourself a fluid with variable density, huh? Talk about fancy! So, let's dive into it, or should I say, sink into it?
According to your equation, the density at any given height, h, is given by p = 45 + ah, where a is 12 kg/m^4. Since we want to find the pressure 10 m below the free surface, let's plug that into the equation.
p = 45 + a * h
p = 45 + 12 * 10
p = 45 + 120
p = 165
So, the pressure at a point 10 m below the free surface in your fluid would be 165 kg/m^3. That's some serious pressure! Just make sure you don't get crushed by it when you take a dive!
To find the pressure at a point 10 m below the free surface in a fluid with variable density, we are given the density function p = 45 + ah.
Step 1: Determine the density at the free surface.
Since the distance measured from the free surface is given, we can substitute h = 0 into the density function:
p = 45 + a(0)
p = 45
Step 2: Find the density at the point 10 m below the free surface.
Substitute h = -10 into the density function:
p = 45 + a(-10)
p = 45 - 120
p = -75
Step 3: Convert the density to pressure.
The pressure at a certain point in a fluid is equal to the density of the fluid multiplied by the acceleration due to gravity (g) and the height (h):
Pressure = Density * g * h
Since we are given the density in kg/m^3, we need to multiply it by the acceleration due to gravity (g) in m/s^2 and the height (h) in meters.
Using the value of g as approximately 9.8 m/s^2, we can find the pressure at the point 10 m below the free surface:
Pressure = -75 kg/m^3 * 9.8 m/s^2 * (-10 m)
Pressure = 7350 N/m^2 (or Pascal)
Therefore, the pressure at a point 10 m below the free surface in the fluid is 7350 N/m^2.
To calculate the pressure at a point 10 m below the free surface in a fluid with variable density given by the equation p = 45 + ah, where a = 12 kg/m^4 and h is the distance measured from the free surface, we can follow these steps:
Step 1: Calculate the value of h for the given point.
Since the point is 10 m below the free surface, h = -10 m.
Step 2: Substitute the value of h into the equation p = 45 + ah.
p = 45 + 12 * (-10)
p = 45 - 120
p = -75
Therefore, the pressure at a point 10 m below the free surface in this fluid is -75 kg/m^3.
It's important to note that the pressure is expressed in units of force per unit area (such as Pascals or N/m^2), not as density (kg/m^3). So, the units for the pressure in this case should be "kg/m^4" instead of "kg/m^3."