The critical velocity of a fluid is the particular velocity at which the liquid flow changes from streamlined to turbulent. For instance, When the velocity of a fluid in a pipe is low, the streamlines are straight parallel lines; however, as the velocity rises, the streamlines remain straight and parallel to the pipe wall until a velocity is achieved which causes the streamlines to break and create patterns.
Vcrit = NRμ/ Dρ
- Vcrit – critical velocity
- NR-Reynolds number
- μ – coefficient of viscosity or resistance to flow in m2/ sec
- D – internal pipe diameter in meter
- ρ – density of the fluid in kg/m2
The critical velocity is calculated using the Reynolds number, which determines whether the flow is streamlined or turbulent. Reynolds number is a variable with no dimensions. It can be calculated using the formula.
If the Reynolds number is between 0 and 2320, the flow is termed streamlined or laminar. A Reynolds number between 2320 and 4000 suggests an unstable flow state ranging from streamlined to turbulent. A Reynolds number greater than 4000 indicates a turbulent flow, implying that the flow velocity is critical.
| Critical velocity | The critical velocity of a fluid is the minimum velocity at which the fluid begins to flow turbulently. |
| Factors affecting | The critical velocity of a fluid is affected by factors such as the fluid’s viscosity, density, and the size and shape of the object the fluid is flowing around. |
| Importance | Understanding the critical velocity of a fluid is important in engineering and fluid dynamics, as it can help to predict and control the behavior of fluids in a variety of applications, such as in pipelines, pumps, and turbines. |
| Calculation | The critical velocity can be calculated using various equations, such as the Reynolds number, which relates the fluid’s density, velocity, viscosity, and length scale. |
| Formula | The formula for the Reynolds number is: Re = ρVD/μ where Re is the Reynolds number; ρ is the density of the fluid; V is the velocity of the fluid; D is the characteristic length scale; μ is the viscosity of the fluid. |
| Daily life examples | Examples of critical velocity in daily life include: the flow of water in a river; the flow of air over the wings of an airplane; the flow of blood through arteries and veins; In each of these cases, understanding the critical velocity of the fluid is important for designing and optimizing the systems that utilize the fluid. |
Table of Contents
Laminar vs Turbulent Flow
When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow (laminar flow or turbulent flow) may occur depending on the velocity, viscosity of the fluid, and the size of the pipe.
Low velocities and high viscosity are conducive to laminar flow. Turbulent flow, on the other hand, occurs at high velocities and low viscosity.
Reynolds Number
In fluid mechanics, the Reynolds number is a criterion for determining whether a fluid (liquid or gas) flow is perfectly steady (streamlined or laminar) or has small unsteady variations on the average (turbulent). Flow in a pipe is generally laminar when the Reynolds number is less than roughly 2,000, but turbulent when the Reynolds number exceeds 2,000.
Actually, the transition from laminar to turbulent flow happens over a wide range of Reynolds numbers, mainly between 1,000 and 2,000 and rising to between 3,000 and 5,000.
Solved Numerical Problem
Problem: A pipe has a diameter of 5 cm and carries water at a temperature of 20°C. What is the critical velocity of the water in the pipe, assuming a viscosity of 1.002 x 10^-3 Pa·s and a density of 998 kg/m^3?
Solution:
- Determine the characteristic length scale of the system, which in this case is the pipe diameter, D = 0.05 m.
- Calculate the Reynolds number using the formula Re = ρVD/μ, where ρ is the density of the fluid, V is the velocity of the fluid, D is the characteristic length scale, and μ is the viscosity of the fluid.
Re = (998 kg/m^3)(V)(0.05 m) / (1.002 x 10^-3 Pa·s) - Set the Reynolds number equal to the critical Reynolds number for the onset of turbulence, which is typically around 2300 for a circular pipe:Re = 2300
- Solve for the critical velocity, V:V = (2300)(1.002 x 10^-3 Pa·s) / (998 kg/m^3)(0.05 m)V ≈ 1.17 m/s
Summary
- Critical velocity is the minimum velocity required for a particular object or fluid to overcome a certain resistance or force.
- At velocities below the critical velocity, the object or fluid will be unable to overcome the resistance and will eventually come to a stop.
- The resistance or force that must be overcome can take various forms, such as friction or buoyancy.
- Critical velocity is often used in the context of fluid dynamics, where it refers to the velocity at which the flow of a fluid transitions from laminar to turbulent.
- In this context, turbulent flow is characterized by chaotic, unpredictable movement and increased drag, while laminar flow is smooth and streamlined.
- The critical velocity for fluid flow depends on factors such as the viscosity and density of the fluid, the diameter of the pipe or channel through which it is flowing, and the roughness of the surfaces in contact with the fluid.
- In practical applications, it is important to be aware of the critical velocity of a system in order to avoid potential issues such as blockages, clogs, or equipment failure.
Related Topics
Velocity Formula & Definition
Velocity Time Graph
How to Find Instantaneous Velocity
Can Velocity be Negative?
Kinematic Equations| Sample Problems and Solutions
Momentum Equation| Definition and Examples
Multiple Choice Questions
- What happens when a fluid is flowing below its critical velocity?
A) The fluid flows smoothly and steadily
B) The fluid flow becomes turbulent
C) The fluid flow is obstructed by viscosity
D) The fluid comes to a stop
Answer: A) The fluid flows smoothly and steadily
- What are some factors that can influence the critical velocity of fluid flow?
A) The length and width of the fluid container
B) The temperature and pressure of the fluid
C) The viscosity and density of the fluid
D) The color and odor of the fluid
Answer: C) The viscosity and density of the fluid
- How is critical velocity related to drag force in fluid flow?
A) As critical velocity increases, drag force decreases
B) As critical velocity increases, drag force increases
C) Drag force is only present in laminar flow
Answer: B)
Frequently Asked Questions
1. What is the viscosity of water?
The viscosity of water at 20 degrees Celsius is 0.01 poise or 0.001 Pa.s (Pascal seconds).
2. What is the definition of viscosity?
The resistance to the flow of a fluid and the resistance to the movement of an object through a fluid is typically expressed in terms of the fluid’s viscosity.
3. Fluid friction?
Fluids exert a resisting force on objects moving through them. This resisting force is called fluid friction.
4. Hydro turbines?
Hydro turbines are devices used in hydroelectric power plants to transfer energy from flowing water to a rotating shaft and generate electricity. In response to the infusion of water into their blades, these turbines revolve or spin.
5. Heat engine?
A heat engine is a device that transforms heat from a source into mechanical work that may be used for a variety of applications.
6. Diffusion coefficient?
The Diffusion coefficient (D), also known as mass diffusivity, is a measurement of how quickly one material diffuses through another.