Formulas for Heat Exchanger System using a Modulating Control Valve HEAT EXCHANGER FORMULAS & EXAMPLE
Formula 6: Steam Load (Q S ) as function of Heat Load Q S = E LH
The steam load or capacity ( Q S in lbs/hr) is dependent on the heat load ( E in Btu/hr) and the latent heat ( LH in Btu/lb) the steam contains. The Latent Heat of saturated steam is dependent on the steam pressure. Consult the Saturated Steam Table in Engineering Section. LH is typically approximated to 1,000 Btu/lb.
Formula 7: Steam Load (Q S ) as function of Water Flow Rate Q S = Q W x500x(T o – T i ) Q S = Q W x Δ T W LH 2
(approximation for LH = 1,000 Btu/lb)
This formula is derived by substituting the right side of Formula 5 for E in Formula 6 . It can be used for calculating the steam load directly from the flow rate of water to be heated.
Formula 8: Water Flow Rate (Q w ) as function of Heat Load Q W = E 500 x (T o – T i ) This formula is derived by solving Formula 5 for Q w . It is useful for determining the water flow rate thru the HX at the stall point ( Q w-stall ). This is explained in the following HX example (see part M).
Formula 9: Percent Stall Load % Stall Load = T B – T WM x 100
Where T WM = T o + T i
T S – T WM 2 This formula is used to calculate the percentage of Full Heat Load ( E D ) at which heat exchanger stall will occur. Since water flow rate is proportional to heat load (see Formula 8 ), the % Stall Load can be used to calculate the water flow rate at stall (see Formula 10 ).
Formula 10: Water Flow Rate at Stall (Q w-stall ) Q w-stall = Q w-full load x (% Stall Load)/100
Where, Q w-full load = Water flow rate at design (maximum) heat load ( E D ) = Maximum water flow rate This formula is used in conjunction with Formula 9 to calculate the water flow rate at which heat exchanger stall will occur without having to know the size of the HX.
Formula 11: Control Valve Steam Capacity (Q S ) at Sub-Critical Flow For Δ P < 0.42 P 1 : 11a : Q S = 2.1 C v 11b : C v = Δ P (P 1 + P 2 )
Q S
Δ P (P 1 + P 2 )
2.1
These formulas are applied when the pressure drop across the control valve ( Δ P ) is less than the critical pressure drop ( 0.42 P 1 ).
Formula 12: Control Valve Steam Capacity (Q S ) at Critical Flow For Δ P > 0.42 P 1 : 12a : Q S = 1.71 C v P 1 12b : C v = Q S 1.71 P 1
When the pressure drop across the valve ( Δ P ) is greater than or equal to the critical pressure drop ( 0.42 P 1 ), the steam capacity ( Q S ) depends only on the valve inlet pressure ( P 1 ). The flow rate at this condition is called the critical flow. For a constant inlet pressure, the critical flow is the maximum capacity of the valve. The above formulas are derived from Formula 11a by using the critical pressure drop ( Δ P = 0.42 P 1 ) and differential pressure ( Δ P = P 1 – P 2 ) formulas to eliminate Δ P and P 2 from the equation. Note: Formulas 11 and 12 are simplified versions of the steam flow equation.
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