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).

Rotational Kinetic Energy can be defined as the kinetic energy associated with rotational motion of an object.  kinetic energy = 1/2 (mv²)  we all know that every particle in an object has same angular speed ω, and tangential speed depends on the distance r from the axis of rotation. Total kinetic Energy of rotating object is the sum of kinetic energy of all individual particles of an object.

so Rotational kinetic energy (K_R) = ∑ 1/2 (mv²) = 1/2 ∑ (m r² ω²) = 1/2 (∑ m r²) ω².

We can also write it as K_R = 1/2 Iω².——- (Moment of Inertia (I)= ∑ m r² ).

Rotational kinetic energy (K_R) = 1/2 Iω²

Mathematically.

Rotational kinetic energy (K_R) = 1/2 (Moment of Inertia x (Angular velocity)²)

Now we know,

Dimensional Formula of Moment of Inertia= M¹L²T⁰
Dimensional Formula of Angular Velocity = M⁰L⁰T^-1

Putting these values in above equation we get

So Dimensional Formula of Rotational kinetic energy = M¹L²T^-2
SI unit of Rotational kinetic energy is Joule (J).