HVAC & thermodynamics

1. Air duct velocity & equivalent diameter
2. Air duct friction pressure drop
3. Heat recovery wheel effectiveness
4. SCFM to ACFM converter
5. Heat exchanger LMTD & area sizing
6. Hot air balloon lifting force
7. Building envelope U-factor & heat loss

$$v=\frac{Q}{A},\qquad D_{eq}=1.30\frac{(ab)^{0.625}}{(a+b)^{0.25}}$$

Equivalent round duct for rectangular cross-sections (Huebscher). Source: Engineering ToolBox.

$$\Delta p_f=\left(\frac{0.10913\cdot Q^{1.9}}{D_{eq}^{5.02}}\right)L$$

Static pressure drop in galvanised steel ducts. $Q$ in m³/s, $D_{eq}$ in m, $L$ in m. Source: Engineering ToolBox.

$$\varepsilon=\frac{T_{\text{supply,out}}-T_{\text{supply,in}}}{T_{\text{exhaust,in}}-T_{\text{supply,in}}}$$

Sensible effectiveness of rotary thermal wheels and run-around coils. Source: Engineering ToolBox & ASHRAE Handbook.

$$\text{ACFM}=\text{SCFM}\cdot\left(\frac{P_{\text{std}}}{P_{\text{act}}-P_v}\right)\cdot\left(\frac{T_{\text{act}}}{T_{\text{std}}}\right)$$

Std ref: 14.7 psia, 60°F. Elevation correction via barometric formula. Source: Engineering ToolBox.

$$\Delta T_{\text{LMTD}}=\frac{\Delta T_1-\Delta T_2}{\ln(\Delta T_1/\Delta T_2)},\qquad Q=UAF\Delta T_{\text{LMTD}}$$

Counter-flow: $\Delta T_1=T_{h,in}-T_{c,out}$, $\Delta T_2=T_{h,out}-T_{c,in}$. $F\approx1$ for single-pass counter-flow. Source: Engineering ToolBox.

$$F_{\text{net}}=gV\left(\rho_{\text{amb}}-\rho_{\text{int}}\right)=gV\frac{P}{R}\left(\frac{1}{T_{\text{amb}}}-\frac{1}{T_{\text{int}}}\right)$$

Net buoyant force from heated air at ambient pressure. $R=287$ J/kg·K for dry air. Source: Engineering ToolBox.

$$R_{\text{total}}=R_{si}+\sum\frac{d_i}{k_i}+R_{se},\quad U=\frac{1}{R_{\text{total}}},\quad Q=UA(T_{\text{in}}-T_{\text{out}})$$

$R_{si}\approx0.13$, $R_{se}\approx0.04$ m²·K/W (internal/external surface resistances). Source: Engineering ToolBox.