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A dimensionless number which is a ratio of kinematics viscosity to thermal diffusivity is known as?
The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivity and can be expressed asPr = v / αThe Prandtl number can alternatively be expressed asPr = μ cp / kThe Prandtl Number is often used in heat transfer and free and forced convection calculations. where:ν : kinematic viscosity, ν = μ / ρ, (SI units : m2/s)α : thermal diffusivity, α = k / (ρcp), (SI units : m2/s)μ : dynamic viscosity, (SI units : Pa s)k: thermal conductivity, (SI units : W/(m K) )cp : specific heat, (SI units : J/(kg K) )ρ : density, (SI units : kg/m3 ).answered by : eng_moom
What is prandtl number and what is its significance?
Prandtl number is dimensionless number, denoted by Npr.Npr = Cp (viscosity)/(thermal conductivity) Cp - specific heat, J per ( Kg Kelvin) viscosity in poise (gm per( cm sec)) thermal conductivity in Watt per (meter kelvin) Prandtl number is important in heat transfer.
Is relative dielectric constant dimensionless?
Correct: it is a dimensionless number.
How do you prove dimensionless groups?
A dimensionless number has no units. The units of all variables that compose the dimensionless number (product or ratio) must cancel each other.
What is dimensionless numbershow and why are they used in heat transfer?
A dimensionless number is a quantity that is normalized as to negate the differences in properties from one substance to another. They are used to enable scientists and engineers to make direct comparisons between dissimilar substances. An example, commonly used in both Fluid Dynamics and Heat Transfer is the Reynolds number expressed as Re = density*velocity*L/mu or Re = velocity*L/nu, where L is the characteristic length, mu is the dynamic viscosity, and nu is the kinematic viscosity. Using the Reynolds number, comparisons between two dissimilar substances (e.g. Glycerine, Water, Alcohol, and Blood) can be made. The nussalt number in heat transfer is a dimenssionaless number and it is the ratio of conductive to convective heat transefer across a boundary.
Which dimensionless quantity has unit?
If a quantity is "dimensionless", that means it has no units, and it's just a number.
Why is Reynold's number dimensionless?
Reynold's number is dimensionless because it is a ratio of inertial forces to viscous forces in a fluid flow. It is calculated using the fluid's density, velocity, characteristic length, and dynamic viscosity, which combine to form a unitless value. This characteristic allows it to be universally applicable across different fluid systems, enabling comparison of flow regimes regardless of the specific units used.
Does a dimensionless quantity have a unit?
No, a dimensionless quantity does not have a unit because it represents a pure number without any physical dimension. Examples of dimensionless quantities include ratios, proportions, and mathematical constants.
How is the Reynolds number derivation calculated for fluid flow analysis?
The Reynolds number derivation for fluid flow analysis is calculated by dividing the product of the fluid velocity, characteristic length, and fluid density by the fluid viscosity. This dimensionless number helps determine the flow regime of a fluid, whether it is laminar or turbulent.
What are the dimensions of 32?
32 is a pure number (integer) and is dimensionless.
What is the importance of Dimensionless numbers?
Dimensionless numbers allow you to compare two systems that are vastly different by combining the parameters of interest. For example, the Reynolds number, Re = velocity * length / kinematic viscosity. If you are testing an airfoil with a particular Re, and you want to run a simulation on a scaled-down model (length is smaller), you could increase fluid velocity or lower kinematic viscosity (change fluids) or both to establish the same Re and ensure you are working under comparable circumstances.
What number is equivalent to 1 cup?
A pure dimensionless (without units) number is never equivalent to a number with a unit.
