Bernoulli's Equation with a ping pong ball

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SUMMARY

The discussion focuses on applying Bernoulli's Equation to analyze the forces acting on a ping pong ball suspended by a hair dryer. The mass of the ping pong ball is approximately 2.7 grams, and the pressure underneath the ball is 1 atm. The upward vertical force required to suspend the ball is calculated using the formula P=F/A, leading to a force of approximately 0.005 Newtons. The complexities of calculating the pressure above the ball and the average speed of the air involve considerations of drag force, turbulence, and the coefficient of drag for a sphere.

PREREQUISITES
  • Understanding of Bernoulli's Equation
  • Knowledge of pressure calculations (P=F/A)
  • Familiarity with drag force concepts
  • Basic principles of fluid dynamics
NEXT STEPS
  • Study the application of Bernoulli's Equation in fluid dynamics
  • Learn about calculating drag force for spherical objects
  • Research the effects of turbulence on airflow
  • Explore the relationship between pressure and velocity in fluid systems
USEFUL FOR

Students studying physics, particularly those focusing on fluid dynamics, engineers working with airflow systems, and anyone interested in practical applications of Bernoulli's Equation.

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Homework Statement



There is a ping pong ball being lifted and suspended in the air by a hair dryer. A.)What is the upward vertical force needed to suspend the ping pong ball? A ping pong ball has a Mass of about 2 grams. B.)If the pressure underneath and inside the ping pong ball is 1 atm what is the pressure above the ping pong ball in Newtons per square meter and C.)what is the average speed of the air in m/sec.

Homework Equations



Bernoulli: P+(1/2)ρV^2+mgh= P+(1/2)ρV^2+mgh
P=F/A

The Attempt at a Solution


For A.) I started with P=F/A and i assumed that the Pressure would be that of 1 Atm and the area of a ping pong ball would be around .005 m^2 based on experience. So the force I got was .005 Newtons. I feel that I am extremely off.
For B and C) I used the bernoulli equation but mixed and matched symbols and somehow got huge numbers. A walk through of how to approach this problem would be greatly appreciated.
 
Physics news on Phys.org
The size of an official ping pong ball is 40 mm, and the mass is 2.7 grams. If the ball is hovering, then the drag force equals the weight of the ball, about 26.5 N, but part of the drag is due to increased pressure below the ball and decreased pressure above the ball.

It ends up complicated, since the coefficient of drag for a sphere depends on smoothness, wind speed, and the size of the ball, and there are issues like turbulence. Link to Nasa article:

http://www.grc.nasa.gov/WWW/K-12/airplane/dragsphere.html
 

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