Space time τ is defined as the volume divided by volumetric flow rate. Which statement is true about τ?

Space time τ is defined as the volume divided by volumetric flow rate. Which statement is true about τ?

• A. It represents the residence time of fluid in a reactor
• B. It is a purely geometric property
• C. It has units of energy
• D. It is always dimensionless

Answer: (A)

Space time is a time-scale that tells you how long, on average, a fluid element spends inside the reactor at a given flow rate. It’s defined as τ = V / Q, where V is the reactor volume and Q is the volumetric flow rate. Because V has units of volume and Q has units of volume per time, τ has units of time (seconds). This quantity is not purely geometric; while the volume is a geometric property, τ changes with the flow rate. If you increase the volumetric flow rate while keeping the volume fixed, τ decreases, meaning fluid spends less time in the reactor. If you increase the volume with the flow rate fixed, τ increases. The statement that τ represents the residence time of the fluid is the best one because it is the characteristic time scale for material to pass through the reactor. In a steady, well-mixed reactor, the average residence time of fluid elements equals τ. It is not an energy quantity and it is not dimensionless.

Space time is a time-scale that tells you how long, on average, a fluid element spends inside the reactor at a given flow rate. It’s defined as τ = V / Q, where V is the reactor volume and Q is the volumetric flow rate. Because V has units of volume and Q has units of volume per time, τ has units of time (seconds).

This quantity is not purely geometric; while the volume is a geometric property, τ changes with the flow rate. If you increase the volumetric flow rate while keeping the volume fixed, τ decreases, meaning fluid spends less time in the reactor. If you increase the volume with the flow rate fixed, τ increases.

The statement that τ represents the residence time of the fluid is the best one because it is the characteristic time scale for material to pass through the reactor. In a steady, well-mixed reactor, the average residence time of fluid elements equals τ. It is not an energy quantity and it is not dimensionless.