A basketball is pressurized to a gauge pressure of PG = 55 kPa when at the surface of a swimming pool. (Patm = 101 kPa). The ball is then submerged in the pool of water which has a density ρ = 1000 kg/m3. Assume the ball does not change in mass, temperature, or volume as it is submerged. 1) Write an equation for the pressure difference ΔP between the inside and outside of the ball when it is submerged a distance y below the surface of the water. 2)Solve the pressure equation for the depth (in meters) at which the pressure difference between the inside and outside of the ball will become zero. At this depth the pressure inside the basketball is the same as the pressure outside the ball. 3) At what depth, in meters, would the pressure difference between the inside and outside of the ball be zero if the ball were submerged in mercury (ρ = 13,500 kg/m3) instead of in water?
Viscosity
The measure of the resistance of a fluid to flow is known as viscosity. Most fluids have some resistance to motion, the resistance provided by the fluid is called viscosity. This resistance is created by the force of attraction between the fluid molecules. If you pour water through a funnel, it flows easily and quickly, because it has very little resistance. But if you pour honey through a funnel, it may take a little time longer, as the density of honey is high.
Poiseuille's Law
The law of Poiseuille or Poiseuille's equation states that the pressure drop of an incompressible fluid especially a liquid in a laminar flow that passes through a cylindrical tube of length L, radius r, pressure gradient ΔP, and mainly depends on the viscosity of the fluid is nothing but the pressure difference of the layers of fluids. ΔP=P1-P2
Drag Forces
Forces that occur due to the movement of fluid are known as fluid mechanics. Following are the fluids present:
A basketball is pressurized to a gauge pressure of PG = 55 kPa when at the surface of a swimming pool. (Patm = 101 kPa). The ball is then submerged in the pool of water which has a density ρ = 1000 kg/m3. Assume the ball does not change in mass, temperature, or volume as it is submerged.
1) Write an equation for the pressure difference ΔP between the inside and outside of the ball when it is submerged a distance y below the surface of the water.
2)Solve the pressure equation for the depth (in meters) at which the pressure difference between the inside and outside of the ball will become zero. At this depth the pressure inside the basketball is the same as the pressure outside the ball.
3) At what depth, in meters, would the pressure difference between the inside and outside of the ball be zero if the ball were submerged in mercury (ρ = 13,500 kg/m3) instead of in water?
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