Space time (τ) is defined as which of the following?

Space time (τ) is defined as which of the following?

• A. The volume divided by the volumetric flow rate
• B. The ratio of enthalpy to entropy
• C. A dimensionless momentum term
• D. The Reynolds number scaled time

Answer: (A)

Space time is the characteristic time that fluid spends in a reactor at the given flow rate. It is defined as the reactor volume divided by the volumetric flow rate, so τ = V / Q. This means that if you increase the volume while keeping the flow rate the same, the material stays longer in the reactor; if you increase the flow rate while keeping the volume fixed, the material moves through faster and τ decreases. In steady operation, this gives the average residence time for the fluid, and it connects nicely to simple reactor models: for a well-mixed reactor, the mean residence time is V/Q, and for a plug-flow reactor with constant Q, τ = V/Q as well. This concept is useful because many rate-based calculations use τ to relate reactor size and throughput to conversion. The other ideas mentioned—such as a ratio of enthalpy to entropy, a dimensionless momentum term, or a Reynolds-number–scaled time—do not represent a time scale for the fluid’s stay in the reactor, so they don’t define space time.

Space time is the characteristic time that fluid spends in a reactor at the given flow rate. It is defined as the reactor volume divided by the volumetric flow rate, so τ = V / Q. This means that if you increase the volume while keeping the flow rate the same, the material stays longer in the reactor; if you increase the flow rate while keeping the volume fixed, the material moves through faster and τ decreases. In steady operation, this gives the average residence time for the fluid, and it connects nicely to simple reactor models: for a well-mixed reactor, the mean residence time is V/Q, and for a plug-flow reactor with constant Q, τ = V/Q as well.

This concept is useful because many rate-based calculations use τ to relate reactor size and throughput to conversion. The other ideas mentioned—such as a ratio of enthalpy to entropy, a dimensionless momentum term, or a Reynolds-number–scaled time—do not represent a time scale for the fluid’s stay in the reactor, so they don’t define space time.