First Order System Response Calculation
Calculates the thermal response time and time constant for a cylindrical probe using the lumped-capacitance model.
📖 Need the theory? Read the methodology, assumptions, and equations in the full reference guide.
1. Define Input Parameters
2. Engineering Output
Wetted Volume (V)
- m³
- m³
Wetted Surface Area (A)
- m²
- m²
Characteristic Length (Lc)
- m
- m
Biot Number (Bi)
- dimensionless
- dimensionless
Time Constant (tau)
- s
- s
Response Time (tp)
- s
- s
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Download Offline Excel CalculationContext & Assumptions
The first-order system response model characterizes the thermal lag of a sensor or mass when exposed to a step change in fluid temperature. By calculating the time constant and Biot number, engineers can verify if the lumped-capacitance assumption is valid and ensure the sensor reacts quickly enough for safety requirements.
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