The thrust F of a screw propeller is known to depend upon the diameter d, speed of advance \nu ,fluid density p, revolution per second N, and the coefficient of viscosity μ of the fluid. Determine the dimensions of each of the variables in terms of L, M,T, and find an expression for F in terms of these quantities

screw thrust = ML 

Explanation:

thrust of a screw propeller is given by the equation = p x Re

where,

D is diameter

V is the fluid velocity

p is the fluid density

N is the angular speed of the screw in revolution per second

Re is the Reynolds number which is equal to  puD/μ

where p is the fluid density

u is the fluid velocity, and

μ is the fluid viscosity = kg/m.s = M

Reynolds number is dimensionless so it cancels out

The dimensions of the variables are shown below in MLT

diameter is m = L

speed is in m/s = L

fluid density is in kg/ = M

N is in rad/s = L =

If we substitute these dimensions in their respective places in the equation, we get

thrust = M

= M

screw thrust = ML 

This is the dimension for a force which indicates that thrust is a type of force