Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Dimensional analysis – concepts of geometric dimensionless numbers
Question Statement:
Milk is agitated in a tank with a rotating impeller. For this system: X = P/(ρN³D⁵), Y = D²Nρ/μ, Z = DN²/g, where P = power imparted by the impeller to the fluid, N = rate of rotation, D = impeller diameter, g = acceleration due to gravity, ρ = fluid density, μ = fluid viscosity. The X, Y, Z are
Options:
(A) X = Grashof number, Y = Power number, Z = Reynolds number
(B) X = Power number, Y = Reynolds number, Z = Froude number
(C) X = Reynolds number, Y = Froude number, Z = Grashof number
(D) X = Froude number, Y = Grashof number, Z = Power number
Official Answer Key:
B
Step-by-Step Solution & Explanation
X = P/(ρN³D⁵) is the classical Power number (Np), a dimensionless group relating impeller power draw to rotational speed, density and diameter — standard in mixing-vessel design. Y = D²Nρ/μ is the (rotational) Reynolds number, Re = ρND²/μ, comparing inertial to viscous forces for a rotating impeller. Z = DN²/g is the Froude number, Fr = N²D/g, comparing inertial to gravitational forces (relevant to free-surface vortexing in agitated tanks). This matches option (B).
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