Hubble constant can be defined as the ratio of receding velocity of  an extra galactic object to the distance of that object.

Mathematically,

Hubble constant(H_o) = Receding velocity(v)/distance(d) .

Dimensional Formula of Receding velocity = M⁰L¹T^-1
Dimensional Formula of Distance = M⁰L¹T⁰

Putting these values in the given equation we get,

Dimensional Formula of Hubble constant = M⁰L⁰T^-1
SI Unit of Hubble Constant is sec^-1.

Radiation pressure is the pressure associated  with the interaction of electromagnetic radiation on any given surface. In other words Radiation pressure is defined as force per unit area exerted by electromagnetic waves.

Mathematically,

Radiation Pressure = Force / Area =  Intensity of wave (I) / Speed of light(c) .

Dimensional Formula of Intensity of wave = M¹L⁰T^-3
Dimensional Formula of Speed of light = M⁰L¹T^-1

Putting these values in the given equation we get,

Dimensional Formula of Radiation pressure = M¹L^-1T^-2
SI Unit of Radiation pressure is N/m² (newton per square meter)

Energy Density is defined as the amount of energy stored in system or region of space per unit volume.

Mathematically,

Energy Density = Energy / Volume.

Dimensional Formula of Energy = M¹L²T^-2
Dimensional Formula of Volume= M⁰L³T⁰

Putting these values in the given equation we get,

Dimensional Formula of Energy Density=M¹L^-1T^-2
SI unit of Energy Density is  J m^-3 (Joule per cubic meter)

Escape velocity is defined as minimum velocity required to escape from the gravitational pull of the earth.

Mathematically,

Escape velocity (V_e) =  ( 2 G M / r) ^1/2 where

G = Universal Gravitational constant

M = Mass of earth in kg

r= distance to center of earth in meters

Dimensional Formula of Universal Gravitational constant = M^-1L³T^-2
Dimensional Formula of Mass of earth = M¹L⁰T⁰
Dimensional Formula of distance to center of earth = M⁰L¹T⁰

Putting these values in above equation we get,

V_e = ( [M^-1L³T^-2] [M¹L⁰T⁰] / [M⁰L¹T⁰] ) ^1/2

V_e = (M⁰L²T^-2) ^1/2

V_e = M⁰L¹T^-1

Dimensional Formula of Escape velocity (V_e) = M⁰L¹T^-1
SI Unit of Escape velocity(V_e) is ms^-1

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