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 (V_C) = 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,

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

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

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)

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)

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

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).