Verifying Dimensionality of Fall Velocity Equation

In summary, the equation for the fall velocity (terminal velocity) of a particle in a viscous medium is Vt = gd^2(Pp - Pm) / 18u, where Vt is the terminal velocity in m/s, g is the acceleration due to gravity, d is the particle diameter in m, Pp and Pm are the densities of the particle and medium in kg/m^3, and u is the viscosity of the medium in kg/m/s. To determine if this equation is dimensionally homogeneous, one must check if the units on both sides of the equation are equivalent. In this case, the units on the left side are m/s, while the units on the right side are m^3/s
  • #1
jase03
6
1
The equation for the fall velocity (terminal velocity) of a particle of a material in a viscous medium has been derived from theory as:

Vt = gd^2(Pp - Pm) / 18 u

Where: Vt is the terminal velocity in m/s; g is the acceleration due to gravity; d is particle diameter in m; Pp and Pm are the densities of the particle and the medium (respectively) in kg/m^3; u is the viscocity of the medium in kg/m/s (kg.m^-1.s^-1)

Demonstrate if this equation is dimensionally homogeneous or not. Show your working.


Could someone show me how you work this out with the cancelling of units.

My final answer I'm getting - m/s = m/s x m

I don't think I'm correct.


Regards
Jason
 
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  • #2


If you show all your steps in the working one can point out where the mistake is.
 

Related to Verifying Dimensionality of Fall Velocity Equation

1. What is the purpose of verifying the dimensionality of the fall velocity equation?

The purpose of verifying the dimensionality of the fall velocity equation is to ensure that the units of measurement used in the equation are consistent and accurate. This is important for scientific accuracy and to ensure that the equation can be used reliably in calculations and experiments.

2. How is the dimensionality of the fall velocity equation determined?

The dimensionality of the fall velocity equation is determined by examining the units of measurement used for each variable in the equation. These units can then be checked to see if they are consistent and match the expected units for velocity, such as meters per second (m/s).

3. Can the dimensionality of the fall velocity equation change?

Yes, the dimensionality of the fall velocity equation can change if the units of measurement used for the variables are changed. However, as long as the units are consistent and match the expected units for velocity, the equation will still be valid.

4. What happens if the dimensionality of the fall velocity equation is not verified?

If the dimensionality of the fall velocity equation is not verified, it could lead to incorrect results in calculations and experiments. This could also make it difficult to compare the equation with other equations or use it in different contexts.

5. Is verifying the dimensionality of the fall velocity equation necessary for all scientific studies?

Yes, verifying the dimensionality of the fall velocity equation is necessary for all scientific studies that use the equation. This ensures the accuracy and reliability of the equation, and is an important step in the research process.

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