Question

The thrust F of a screw propeller is known to depend upon the diameter d,speed of advance \\u ,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

thrust = ML
`T^(-2)`

Step-by-step explanation:

T = p
`V^(2)`
`D^(2)` x
`(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)`
`(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