Speed is defined as change of distance per unit time. Speed is a scalar quantity.

Mathematically,
Speed  = distance / time .

Dimensional Formula of Distance  = M⁰L¹T⁰
Dimensional Formula of Time = M⁰L⁰T¹

Putting these values in above equation we get,
Dimensional Formula of Speed = M⁰L¹T^-1
SI unit of Speed is ms^-1

Velocity  is defined as the displacement per unit time. It is a vector quantity. The SI unit of Velocity and speed are same. In simple words velocity can be explained as  speed in specific direction.

Mathematically,
Velocity  = displacement / time .

Dimensional Formula of Displacement  = M⁰L¹T⁰
Dimensional Formula of Time = M⁰L⁰T¹

Putting these values in above equation we get,
Dimensional Formula of Velocity = M⁰L¹T^-1
SI unit of Velocity is ms^-1

Viscosity is defined as the ratio of force require to shear a liquid to  the velocity of shear (Shear means when adjacent layers of liquid are made to slide over each other ).

Coefficient of viscosity is defined as tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

Mathematically,
Coefficient of viscosity (η)= Fr/Av    ——- F= tangential Force, Area, r= distance between the layers, v= velocity.

Dimensional Formula of Force = M¹L¹T^-2.
Dimensional Formula of Area= M⁰L²T⁰.
Dimensional Formula of distance= M⁰L¹T⁰.
Dimensional Formula of velocity= M⁰L¹T^-1.

Putting these values in above equation we get,

[η]= [M¹L¹T^-2][M⁰L¹T⁰] / [M⁰L²T⁰] [M⁰L¹T^-1] = [M¹L^-1T^-1]

Dimensional Formula of Coefficient of viscosity (η)=[M¹L^-1T^-1]
SI unit of Coefficient of viscosity (η) is Pascal-second

Distance traveled by the particle in nth second is defined as the difference between the distance travelled by the particle in n second and the distance travelled by the particle in (n-1) second.

Mathematically,
Distance travelled in nth second= Distance/Time.

Dimensional Formula of Distance= M⁰L¹T⁰.
Dimensional Formula of Time= M⁰L⁰T¹.

Putting these values in above equation we get,

Dimensional Formula of Distance traveled in nth second = M⁰L¹T⁰/M⁰L⁰T¹ = M⁰L¹T^-1
SI unit of  Distance traveled in nth second is ms^-1.

Reynolds number is defined as the ratio of dynamic pressure to shearing stress.It is a non dimensional parameter.Reynolds number predicts the extent of turbulence in a fluid, based on how fast the fluid is flowing, the geometry of flow(depth and wide etc…)  density  and viscosity of fluid.

Mathematically,

Reynolds number (Re) = Dynamic Pressure (ρ v²) / Shearing Stress (μ v / L)

Re   = ρ v² / (μ v / L)

Re = ρ v L / μ

where

Re = Reynolds Number (non-dimensional)

ρ = density

v = velocity

μ = dynamic viscosity

L= characteristic length

Dimensional Formula of Density (ρ) =M¹L^-3T⁰
Dimensional Formula of Velocity(v) = M⁰L¹T^-1
Dimensional Formula of Dynamic viscosity(μ) = M¹L^-1T^-1
Dimensional Formula of Length(L) = M⁰L¹T⁰

Putting these values in above equation we get,

Dimensional Formula of Reynolds Number = (M¹L^-3T⁰)(M⁰L¹T^-1)(M⁰L¹T⁰)/(M¹L^-1T^-1)

Dimensional Formula of Reynolds Number = M⁰L⁰T⁰
Reynolds Number has no units (non dimensional).