Answer:
screw thrust = ML[tex]T^{-2}[/tex]
Explanation:
thrust of a screw propeller is given by the equation = p[tex]V^{2}[/tex][tex]D^{2}[/tex] x [tex]\frac{ND}{V}[/tex]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[tex]L^{-1}[/tex][tex]T^{-1}[/tex]
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[tex]T^{-1}[/tex]
fluid density is in kg/[tex]m^{3}[/tex] = M[tex]L^{-3}[/tex]
N is in rad/s = L[tex]L^{-1}[/tex][tex]T^{-1}[/tex] =
If we substitute these dimensions in their respective places in the equation, we get
thrust = M[tex]L^{-3}[/tex][tex](LT^{-1}) ^{2}[/tex][tex]L^{2}[/tex][tex]\frac{T^{-1} L}{LT^{-1} }[/tex]
= M[tex]L^{-3}[/tex][tex]L^{2}[/tex][tex]T^{-2}[/tex]
screw thrust = ML[tex]T^{-2}[/tex]
This is the dimension for a force which indicates that thrust is a type of force
