Show that Reynold's number R=(rhov_(0)d)/(eta)is dimensionless. (rho is density of the fluid, v_(0) is the critical velocity, d is diameter through which the fluid is flowing and eta is the coefficient of viscosity of the fluid).

Show that Reynold's number R=(rhov_(0)d)/(eta)is dimensionless. (rho i

1.	Show that Reynold's number R=(rhov_(0)d)/(eta)is dimensionless. (rho is density of the fluid, v_(0) is the critical velocity, d is diameter through which the fluid is flowing and eta is the coefficient of viscosity of the fluid).
Answer» Solution :`R=([ML^(-3)][LT^(-1)][L])/([ML^(-1)T^(-1)])=[(ML^(-1)T^(-1))/(ML^(-1)T^(-1))]=[M^(0)L^(0)T^(0)]` `therefore R` is dimensionless.