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:

screw thrust = ML$T^{-2}$ 

Explanation:

thrust of a screw propeller is given by the equation = p$V^{2}$$D^{2}$ x $\frac{ND}{V}$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$L^{-1}$$T^{-1}$

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$T^{-1}$

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

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

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

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

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

screw thrust = ML$T^{-2}$ 

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