Critical Velocity Formula
Last Updated :
04 Feb, 2024
The velocity at which gravity and air resistance are equalized on the object is called the critical velocity of a free-fall object. It is the velocity at which the flow of a fluid transition from streamlined to turbulent. The critical velocity of a liquid depends on various factors such as Reynolds number, viscosity coefficient, the radius of the tube and density of the fluid flowing through the tube. It is denoted by the symbol Vc. Its unit of measurement is m/s and the dimensional formula is given by [M0L1T-1].
Formula
Vc = Reη / ρr
where,
Vc is the critical velocity,
Re is the ratio of inertial force to viscous force, that is, Reynolds number,
η is the coefficient of viscosity,
ρ is the density of the fluid,
r is the radius of tube.
Sample Problems
Problem 1. Calculate the critical velocity of a fluid flowing through a tube of radius 2 m. The density and coefficient of viscosity of the fluid are 1.5 kg/m3 and 2 kg/ms respectively. The value of Reynolds number is 1500.
Solution:
We have,
Re = 1500
η = 2
ρ = 1.5
r = 2
Using the formula we get,
Vc = Reη / ρr
= (1500) (2)/ (1.5) (2)
= 3000/3
= 1000 m/s
Problem 2. Calculate the critical velocity of a fluid flowing through a tube of radius 3 m. The density and coefficient of viscosity of the fluid are 2 kg/m3 and 1.5 kg/ms respectively. The value of Reynolds number is 2000.
Solution:
We have,
Re = 2000
η = 1.5
ρ = 2
r = 3
Using the formula we get,
Vc = Reη / ρr
= (2000) (1.5)/ (2) (3)
= 3000/6
= 500 m/s
Problem 3. Calculate the Reynolds number of a fluid flowing through a tube of radius 1 m. The density and coefficient of viscosity of the fluid are 3 kg/m3 and 4 kg/ms respectively. The value of critical velocity is 300 m/s.
Solution:
We have,
Vc = 300
η = 4
ρ = 3
r = 1
Using the formula we get,
Vc = Reη / ρr
=> 300 = Re (4) / (3) (1)
=> Re = 900/4
=> Re = 225
Problem 4. Calculate the Reynolds number of a fluid flowing through a tube of radius 3 m. The density and coefficient of viscosity of the fluid are 5 kg/m3 and 2 kg/ms respectively. The value of critical velocity is 400 m/s.
Solution:
We have,
Vc = 400
η = 2
ρ = 5
r = 3
Using the formula we get,
Vc = Reη / ρr
=> 400 = Re (2) / (5) (3)
=> Re = 6000/2
=> Re = 3000
Problem 5. Calculate the viscosity coefficient of a fluid flowing through a tube of radius 4 m. The density and Reynolds number of the fluid are 5 kg/m3 and 2800 respectively. The value of critical velocity is 200 m/s.
Solution:
We have,
Vc = 200
Re = 2800
ρ = 5
r = 4
Using the formula we get,
Vc = Reη / ρr
=> 200 = (2800) η / (5) (4)
=> η = 4000/2800
=> η = 1.42 kg/ms
Problem 6. Calculate the viscosity coefficient of a fluid flowing through a tube of radius 2 m. The density and Reynolds number of the fluid are 6 kg/m3 and 1000 respectively. The value of critical velocity is 350 m/s.
Solution:
We have,
Vc = 350
Re = 1000
ρ = 6
r = 2
Using the formula we get,
Vc = Reη / ρr
=> 350 = (1000) η / (6) (2)
=> η = 4200/1000
=> η = 4.2 kg/ms
Problem 7. Calculate the density of a fluid flowing through a tube of radius 6 m. The coefficient of viscosity and Reynolds number of the fluid are 5 kg/ms and 2500 respectively. The value of critical velocity is 420 m/s.
Solution:
We have,
Vc = 420
Re = 2500
η = 5
r = 6
Using the formula we get,
Vc = Reη / ρr
=> 420 = (2500) (5) / 6ρ
=> ρ = 12500/2520
=> ρ = 4.96 kg/m3
Like Article
Suggest improvement
Share your thoughts in the comments
Please Login to comment...