Is the formula I developed to calculate the temperature drop of superheated steam correct?

1.4MPa, 240℃, steam； φ159 pipe, aluminum silicate insulation layer, 80mm thick ； Flow rate: 8000 kg/h. Heat loss qw: approximately 109 W/m2. The temperature drop per kilometer calculated using this formula is a little over 10 degrees Celsius.

Your approach to the formula is correct, but adjustments may be needed in terms of units and constants. Based on the formula you provided, it is reasonable to determine the calculations for heat, steam weight, and other aspects. However, it is very important to ensure consistency among various units during the final simplification. In the formula, qw represents the heat loss in watts per square meter (W/m²); the heat amount Q is calculated using the pipe surface area S and the time T during which steam passes through, and this process is correct. There is also no problem with calculating the weight m of the steam. Please note that when calculating the temperature drop, you should ensure that all units are consistent, for example by converting D from millimeters to meters. Moreover, 3600 is the factor used to convert hours to seconds, so this factor must also be taken into account during calculations. Regarding the selection of the specific heat capacity C, as you mentioned, since pressure and temperature changes can affect it, it is a reasonable approach to use an average value for calculation. Overall, your formula framework is correct, but it is recommended to check again the consistency of units and the accuracy of the constants used. .

Kimi replied that the formula you developed for calculating the temperature drop of superheated steam is reasonable, but the following points need to be taken into account: Plausibility of the assumptions: The assumption that no condensate water is formed, meaning the steam remains in a superheated state at all times, is a prerequisite for the formula to hold true. In practical situations, if parameters such as steam conditions or pipe conditions change, condensation may occur, rendering the formula no longer applicable. Unit consistency: When deriving formulas, it is important to ensure that the units of all parameters are consistent in order to maintain the accuracy of the calculation results. For example, the unit of the outer diameter D of a pipe is millimeters (mm); when calculating the surface area S of the pipe, it needs to be converted to meters (m). Change in specific heat capacity: The specific heat capacity C is affected by factors such as steam pressure and temperature, and it varies under different operating conditions. For accurate calculations, the exact specific heat capacity values for the corresponding operating conditions should be used. Other influencing factors: In actual engineering applications, the drop in steam temperature is also affected by a variety of factors, including the insulation of the pipes, the steam flow rate, the material and thickness of the pipes, as well as the ambient temperature. This formula provides only a rough calculation based on known heat loss, specific heat capacity, outer diameter of the pipe, and mass flow rate; more comprehensive analysis and adjustments may be required in practical applications. Below is a brief derivation of the formula along with a unit analysis for your reference: Heat Q: The unit of heat loss qw is W/m²; the unit of the pipe’s surface area S is m², and the unit of time T during which steam passes through the pipe is seconds (s). Heat Q = qw × S × T, with the unit being J (joules). Steam weight m: The unit of mass flow rate G is kg/h; converting this to kg/s gives G/3600. Multiplying this value by time T (in seconds) yields the steam weight m = G×T/3600, with the unit being kg. Temperature difference Δt: The specific heat capacity C is in units of J/(kg・℃). Using the formula Δt = Q/(C×m), and substituting the expressions for Q and m, we get: Δt = (q_w×S×T)/(C×G×T/3600) = (q_w×S×3600)/(C×G). The surface area of the pipe, S = π×D (with D needing to be converted from mm to m, i.e., D/1000 m). Substituting this value gives: Δt = (q_w×π×D/1000×3600)/(C×G) = q_w×π×D×3600/(C×G×1000). When calculating the temperature drop per kilometer, since the pipe length is 1 km = 1000 m, and taking into account unit consistency as well as the impact of the pipe length, the final formula simplifies to Δt per kilometer = q_w×π×D/(C×G×1000) ×3600. Further simplification yields: the temperature drop per kilometer Δt = q_w×3.14×D/(C×G) ×3600 ×1/1000 = q_w×3.14×D/(C×G) ×3.6. Compared to the formula you provided, there are differences in the coefficients, which may be due to unit conversions or inadequate consideration of pipe length during the derivation process. In summary, your calculation formula is theoretically reasonable, but in practical applications it is necessary to pay attention to unit consistency, the accuracy of specific heat capacities, and the comprehensive consideration of various influencing factors. Additionally, careful checks must be carried out during the derivation process regarding unit conversions and coefficient calculations to ensure the accuracy of the formula.

Are there any actual Excel formulas? I’ll match it with our current operating conditions and provide you with some feedback data: lol

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