Experiment on Fluids:
Finding the Velocity of a Fluid in a Confined Container

Purpose:

To calculate the velocity of a confined fluid, given the cross-section area and velocity of another region.

Concept:

The drawing below is a cross-section of a circular cone attached to a circular cylinder.

When a fluid (liquid or gas) is in a confined space, with no change in pressure or temperature, one can use the equation of continuity to find the velocity of the fluid if one knows the cross-section area and velocity in one of the regions. The formula for this is A1*V1 = A2*V2, where A is the cross-section area of one location and V is the velocity for that location.

Analysis:

Given three different locations in a confined container, A, B, and C, all having different radii, can you find the other two velocities of the fluid, if the velocity at A is given?

1. If the cross-section at A has a radius of 6 meters, can you find the area of the slice through the cone
   (Area = pi * r ²)?
   (answer)

    

2. If the velocity of the fluid at location A is 10.0 m/s, and the radius at location B is 4.2 meters, can you find the velocity at location B?
   (answer)

    

3. If the velocity at location C is 8.6 m/s, can you find the radius at location C?
   (answer)

   Extension:

4. If the radius of a fourth location, D, is one-half the radius of A , how would the velocity at location D compare to the velocity of the fluid at A? If D had one-third the radius of A, compare the velocity of the fluid at D to A. Explain your reasoning showing calculations.
   (answer)