# Bernoulli's Equation with a ping pong ball

• shark1818
In summary, the conversation discusses the force and pressure needed to suspend a ping pong ball in the air using a hair dryer. The Bernoulli equation is used to calculate the force needed based on the pressure and area of the ball. The size and mass of an official ping pong ball is also mentioned, along with the complexities of drag force and its relation to smoothness, wind speed, and size. A NASA article is provided as a resource for further information.
shark1818

## 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.

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

## What is Bernoulli's Equation with a ping pong ball?

Bernoulli's Equation is a principle in fluid dynamics that relates the pressure, velocity, and elevation of a fluid. In the case of a ping pong ball, it explains the relationship between the air pressure, velocity, and elevation of the ball as it moves through the air.

## How does Bernoulli's Equation apply to a ping pong ball?

When a ping pong ball moves through the air, it creates a region of high pressure in front of it and a region of low pressure behind it. This difference in pressure creates a net force on the ball, causing it to accelerate and change its velocity.

## What factors affect the application of Bernoulli's Equation on a ping pong ball?

The speed and direction of the ball, the density and viscosity of the air, and the shape and surface of the ball can all affect the application of Bernoulli's Equation on a ping pong ball.

## Can Bernoulli's Equation explain the Magnus effect on a ping pong ball?

Yes, Bernoulli's Equation can help explain the Magnus effect, which is the phenomenon where a spinning object experiences a lift force perpendicular to the direction of motion. In the case of a ping pong ball, the spin creates a difference in air pressure, causing the ball to curve in flight.

## How is Bernoulli's Equation used in practical applications with ping pong balls?

Bernoulli's Equation is used to design and improve the flight of ping pong balls in sports such as table tennis. It is also used in the development of aerodynamic equipment for ping pong, such as paddles and balls, to optimize their performance.

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