Question

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

Answer 1

Answer:

thrust = ML$T^{-2}$  

Explanation:

T = p$V^{2}$$D^{2}$ x $\frac{ND}{V}$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$L^{-1}$$s^{-1}$

Reynolds number is dimensionless so it cancels out

diameter is m = L

speed is in m/s = L$T^{-1}$

fluid density is in kg/$m^{3}$ = M$L^{-3}$

N is in rad/s = L$L^{-1}$$T^{-1}$ = $T^{-1}$

combining these dimensions into the equation, we have

thrust = M$L^{-3}$$( LT^{-1}) ^{2}$$L^{2}$$\frac{T^{-1}L }{LT^{-1} }$

= M$L^{-3}$$L^{2}$$T^{-2}$$L^{2}$

thrust = ML$T^{-2}$   which is the dimension for a force which indicates that thrust is a type of force