How Can Bernoulli's Equation Explain a Floating Ball?

[smither777]

Hi,

I need help with a project on Bernoulli's floating ball. I wanted to prove with the use of Bernoulli's equation that the the velocity or pressure in one side of the equation (the low pressure area) is lower in pressure or higher in velocity.

This is what I have so far:
Using: P1 + 1/2pv1^2 = P2 + 1/2pv2^2 , where P1 is the High Pressure area (atmospheric pressure), p = density of the gas, v = velocity and where P2 is the Low Pressure area (the air from the pump that makes the ball float).

I was able to obtain the variables for the High PRessure area:
P1 = 101.3 KPa
p = 1.29 kg/m^3
v = 0 m/s

However, I have a problem now for obtaining the variables in the Low Pressure area...
P2 = ? (i could obtain this one instead of velocity..)
p = 1.29 kg/m^3
v = ? (i could obtain this one instead of Pressure)

I don't know now how to obtain either Pressure or the velocity of the fluid that's in the low pressure area... please help.. thank you.

 

[Clausius2]

I have not understood nothing.

 

[charng]

Hello,

Bernoulli's equation relates the pressure, velocity, and height of a fluid in a horizontal flow. In order to use this equation to explain the floating ball, we need to consider the Bernoulli's equation in two different points: at the surface of the ball and at the surface of the liquid.

At the surface of the ball, the flow is horizontal and the velocity is zero. This means that the first term on the right side of the equation (1/2pv1^2) becomes zero. We can then rewrite the equation as P1 = P2 + 1/2pv2^2.

At the surface of the liquid, the flow is also horizontal and the pressure is equal to the atmospheric pressure (P1 = 101.3 KPa). The density of the liquid (p) is also known. This means that we can solve for the velocity (v) at this point by rearranging the equation to v2 = √[(2(P1-P2))/p].

To find the pressure at the surface of the liquid (P2), we can use the ideal gas law which states that P2V2 = P1V1, where V1 and V2 are the volumes of the gas at the two different pressures. Since the volume of the gas is constant, we can rewrite the equation as P2 = (P1V1)/V2. The volume of the gas at the surface of the ball (V1) can be calculated using the volume of the ball and the height of the liquid it displaces. The volume of the gas at the surface of the liquid (V2) is equal to the volume of the ball.

I hope this helps you in obtaining the variables for the low pressure area. Remember, Bernoulli's equation only applies to horizontal flow, so make sure to consider the flow at both points. Best of luck with your project!