Answer:
thrust = ML[tex]T^{-2}[/tex]
Explanation:
T = p[tex]V^{2}[/tex][tex]D^{2}[/tex] x [tex]\frac{ND}{V}[/tex]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[tex]L^{-1}[/tex][tex]s^{-1}[/tex]
Reynolds number is dimensionless so it cancels out
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] = [tex]T^{-1}[/tex]
combining these dimensions into the equation, we have
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][tex]L^{2}[/tex]
thrust = ML[tex]T^{-2}[/tex] which is the dimension for a force which indicates that thrust is a type of force
