PLEASE HELP in Deriving Terminal Velocity Equation

In summary, the conversation discusses the derivation of the terminal velocity equation, which is given by v = sqrt(2mg/DρA). The participants also discuss how to ensure the equation is dimensionally correct and how to estimate the terminal velocity of an Australian $1 coin. They suggest using dimensional analysis to determine the dimensions of each symbol in the equation, as well as looking up values for the density of air and the mass and area of the coin.
  • #1
hibachii
17
0
PLEASE HELP! in Deriving Terminal Velocity Equation :)

Homework Statement



The terminal velocity of a mass m, moving at 'high speeds' through a fluid of density
ρ(kg m^-3), is given by v = sqrt(2mg/DρA) where A is the cross sectional area of the object (m^2) and D a dimensionless "drag coefficient".

i) Show that equation is dimensionally correct
ii) Estimate the terminal velocity of an Australian $1 coin. Take D to be ~0.3.

Homework Equations



v = sqrt(2mg/DρA)

The Attempt at a Solution



I'm completely stuck. I have no clue as in how to even start. I'm so sorry :(
 
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  • #2
welcome to pf!

hi hibachii! welcome to pf! :smile:

(have a square-root: √ and try using the X2 tag just above the Reply box :wink:)

what are the dimensions of each symbol in √(2mg/DρA)?

check that when you combine them they come to the same as v :wink:
 
  • #3


I'm going to assume your in the same Physics Class as I am.

If you go to Page 7 of the the book "Physics for Scientists and Engineers" by Serway it explains how to do Dimensional Analysis and that will explain how to do (i).

For (ii) you will need to look up a value for the density of air and then estimate the mass and area of the coin remembering that the coin would be rotating as it fell through the air
 
  • #4


Cheers guys. Helped alot.

P.S Jazrad what class are you in for physics 101?
 
  • #5


Hey jazrad thanks but I am still stuck. I've looked at page 7 and 8 but it only shows dimensions for velocity and acceleration. I've still got a lot of unknowns like D, A, m and ρ.
I tried subbing in L/T for v and L/T^2 for g but I am still left stuck. Please give some more help although you have provided me with a very good start.
Cheers
 
  • #6
hey hibachii! :smile:

(try using the X2 icon just above the Reply box :wink:)
hibachii said:
Ive still got a lot of unknowns like D, A, m and ρ.

(D is given as dimensionless :wink:)

to find the dimensions of an unfamiliar variable, decde what units it's measured in (m/s2 for example), then convert each unit to dimensions (m/s2 = L/T2)

start with ρ, the density …

what units is it measured in? :smile:​
 

FAQ: PLEASE HELP in Deriving Terminal Velocity Equation

1. What is terminal velocity?

Terminal velocity is the maximum velocity that an object can reach when falling through a fluid, such as air or water. It occurs when the upward force of air resistance equals the downward force of gravity.

2. How is terminal velocity calculated?

The terminal velocity equation is v = sqrt((2mg)/(ρAC)), where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the projected area of the object, and C is the drag coefficient.

3. What factors affect terminal velocity?

The factors that affect terminal velocity include the mass and shape of the object, the density and viscosity of the fluid, and the force of gravity. Additionally, the presence of other forces, such as wind or buoyancy, can also affect terminal velocity.

4. How does air resistance impact terminal velocity?

Air resistance, also known as drag, is the force that opposes the motion of an object through a fluid. As an object accelerates due to the force of gravity, air resistance increases until it becomes equal to the force of gravity, resulting in a constant terminal velocity.

5. Why is the terminal velocity equation important?

The terminal velocity equation is important because it allows us to calculate the maximum speed at which an object will fall through a fluid, which is useful in various fields such as physics, engineering, and aerodynamics. It also helps us understand the effects of air resistance and other factors on the motion of objects.

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