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

thrust = ML  

Explanation:

T = p x Re

where D is diameter

p is the density

N is the 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

μ is the fluid viscosity = kg/m.s = M

Reynolds number is dimensionless so it cancels out

diameter is m = L

speed is in m/s = L

fluid density is in kg/ = M

N is in rad/s = L =

combining these dimensions into the equation, we have

thrust = M

= M

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