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What is Dimensional Formula of Critical velocity ?

Critical velocity is defined as the maximum velocity of a fluid above which a streamline flow changes to turbulent flow. In other words critical velocity the maximum velocity of fluid upto which its flow remains streamline and if the velocity of a fluid increases more than its critical velocity the flow of fluid becomes turbulent.

Mathematically,

Critical velocity (VC) = Re   η /  ρ  r    

where

Re = Reynolds number

η = coefficient of viscosity

ρ = density of fluid

r = radius of tube.
Dimensional Formula of Reynolds number (Re) = M0L0T0
Dimensional Formula of coefficient of viscosity (η) =  M1L-1T-1
Dimensional Formula of Density of fluid (ρ) =M1L-3T0
Dimensional Formula of radius (r) = M0L1T0

Putting these values in above equation we get,

VC = [M0L0T0] [M1L-1T-1] / [M1L-3T0] [M0L1T0]

Dimensional Formula of Critical velocity(VC) = M0L1T-1
SI unit of Critical velocity(VC) is ms-1

posted in Dimensional Formulae | 6 Comments

What is Dimensional Formula of moment of couple?

Moment of couple is defined as the product of perpendicular distance between the forces and magnitude of the force.

Mathematically,

Moment of couple = Force x Distance

Dimensional Formula of Force= M1L1T-2
Dimensional Formula of Distance = M0L1T0

Putting these values in the given equation we get,

Dimensional Formula of moment of couple = M1L2T-2
SI unit of moment of couple is Newton metre (N m)

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What is Dimensional Formula of moment of force?

The moment of force is defined as the tendency to produce rotation of object on its axis.

Mathematically,

Moment of force=Force x Distance

Dimensional Formula of Force= M1L1T-2
Dimensional Formula of Distance = M0L1T0

Putting these values in the given equation we get,

Dimensional Formula of moment of force = M1L2T-2
Si unit of moment of force is Newton metre (N m)

posted in Dimensional Formulae | 2 Comments

What is Dimensional Formula of Pressure Gradient?

Pressure Gradient is defined as the change in pressure per unit distance. In other words pressure change over a unit distance is known as Pressure Gradient.

Mathematically,
Pressure Gradient = Pressure / Distance.

Dimensional Formula of Pressure = M1L-1T-2
Dimensional Formula of Distance= M0L1T0

Substituting the values in the given equation we get,

Dimensional Formula of Pressure Gradient = M1L-2T-2
SI unit of Pressure Gradient is Nm-3

posted in Dimensional Formulae | 2 Comments

What is Dimensional Formula of Pressure Energy?

Pressure Energy can be defined as the energy possessed by a fluid by virtue of its pressure. In simpler words the energy acquired by a fluid by applying pressure on the fluid is known as Pressure Energy.

Mathematically,
Pressure Energy = Pressure X volume.

Dimensional Formula of Pressure = M1L-1T-2
Dimensional Formula of Volume= M0 L3 T0

Substituting the values in the given equation we get,

Dimensional Formula of Pressure Energy = M1 L2 T-2
SI unit of Pressure Energy is Joule (J).

posted in Dimensional Formulae | 1 Comment