Question

A liquid of density ρ and coefficient of viscosity η flows with velocity v through a tube of diameter D. A quantity `"R" = (rho"vD")/η`, determines whether the flow will be streamlined or turbulent. R has the dimension of ______.

Options

• velocity

• acceleration

• force

• None of these

Answer 1

None of these

Explanation:

Given, quantity, `"R" = (rho"vD")/η`

Here, the dimension of density, ρ = [ML^-3T⁰]

Dimensions of velocity, v = [M⁰LT^-1]

Dimension of diameter, D = [M⁰LT⁰]

and the dimension of coefficient of viscosity, η = [ML^-1T^-1]

∴ Dimensions of R = `(["M""L"^-3"T"^0]["M"^0"L""T"^-1]["M"^0"L""T"^0])/(["M""L"^-1"T"^-1]) = ["M"^0"L"^0"T"^0]`

Hence, R has no dimensions.