Acceleration with Fluid Resistance

The Acceleration with Fluid Resistance calculator computes the acceleration of an object accelerating with the force of gravity in a fluid.  The fluid exerts a resistive force on the object's motion.

INSTRUCTIONS: Choose units and enter the following:

• (k) - This is the constant of proportionality for the resistive force
• (m) - This is the mass of the accelerating object
• (t) - This is the time after the object started accelerating when we are measuring the acceleration

The Math / Science

The formula for the Acceleration with Fluid Resistance is:

       `a_y = g*e^((-k/m)t)`

where:

• a_y is the acceleration with fluid resistance
• g is the acceleration due to gravity
• k is the constant of proportionality for the resistive force
• m is the mass
• t is the time duration

This is based on the equation for the resistive force of a fluid at low speeds^{[ 1 ]} :

   F = k•v, where v is the body's speed

Sources

Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 157, eq 5.11

1. ^ Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 155, eq 5.7