What best describes the power number in mixing?

What best describes the power number in mixing?

• A. The Reynolds number of a flow in a pipe
• B. A dimensionless group relating impeller power to fluid properties and geometry
• C. It is the ratio of piston displacement to cylinder volume
• D. A measure of pressure drop in a pipe

Answer: (B)

The power number is a dimensionless group that ties the power input to the impeller to the fluid’s density, the rotation speed, and the impeller size. It is defined as Np = P / (ρ N^3 D^5), where P is the impeller power, ρ is the fluid density, N is the rotation speed, and D is the impeller diameter. This single number captures how geometry and flow regime influence how much energy is put into the fluid for a given operating condition. In practice, Np allows us to compare and scale mixing systems. For a given impeller and liquid, the power you need scales with ρ, N^3, and D^5, while Np encodes the effects of impeller design and whether the flow is laminar or turbulent. As you scale up a mixer, you can keep Np roughly the same under similar conditions, and use P ≈ Np · ρ · N^3 · D^5 to estimate the required power. The other statements describe different concepts: Reynolds number, a measure of inertial versus viscous forces in a flow; a piston displacement-to-cylinder volume ratio, which is a compression-related metric; and pressure drop, a loss term in piping. These are not what the power number represents.

The power number is a dimensionless group that ties the power input to the impeller to the fluid’s density, the rotation speed, and the impeller size. It is defined as Np = P / (ρ N^3 D^5), where P is the impeller power, ρ is the fluid density, N is the rotation speed, and D is the impeller diameter. This single number captures how geometry and flow regime influence how much energy is put into the fluid for a given operating condition.

In practice, Np allows us to compare and scale mixing systems. For a given impeller and liquid, the power you need scales with ρ, N^3, and D^5, while Np encodes the effects of impeller design and whether the flow is laminar or turbulent. As you scale up a mixer, you can keep Np roughly the same under similar conditions, and use P ≈ Np · ρ · N^3 · D^5 to estimate the required power.

The other statements describe different concepts: Reynolds number, a measure of inertial versus viscous forces in a flow; a piston displacement-to-cylinder volume ratio, which is a compression-related metric; and pressure drop, a loss term in piping. These are not what the power number represents.