Let's break down the **problem step by step** and solve it **in English**. --- ## **Problem Statement (English Translation)** - **530 cfm** of outside air (at 95°F, 78° F bh) mixes with **1550 cfm** of return air from the room (at 75°F, 66°F bh). - The air that leaves the air conditioning unit is at 57°F, 56°F bh. - **Question:** How much air (cfm) exits the air conditioner **at the same conditions** as after passing through the unit, assuming the coil surface temperature is 55°F? --- ## **Step 1: Find the Total Mixed Airflow** Total mixed air = outside air + return air \[ Q_{mixed} = 530\, \text{cfm} + 1550\, \text{cfm} = 2080\, \text{cfm} \] --- ## **Step 2: Understand the Question** The question asks: *How much air can be cooled to 57°F and 56°F bh (i.e., saturated or nearly saturated air at that condition), given the coil surface temperature is 55°F?* This is a **bypass factor** or **coil ADP (Apparatus Dew Point)** problem. --- ## **Step 3: Find the Bypass Factor** ### **Bypass Factor (BF) Formula:** \[ BF = \frac{T_{out} - T_{coil}}{T_{mix} - T_{coil}} \] Where: - \( T_{out} \): Leaving air temperature = 57°F - \( T_{coil} \): Coil surface temperature = 55°F - \( T_{mix} \): Mixed air temperature (to be calculated) --- ## **Step 4: Calculate the Mixed Air Temperature (Tmix)** \[ T_{mix} = \frac{(530 \times 95) + (1550 \times 75)}{2080} \] \[ T_{mix} = \frac{50350 + 116250}{2080} = \frac{166600}{2080} \approx 80.1^\circ F \] --- ## **Step 5: Calculate the Bypass Factor** \[ BF = \frac{57 - 55}{80.1 - 55} = \frac{2}{25.1} \approx 0.08 \] --- ## **Step 6: Find the Proportion of Air Cooled to Coil Temperature (55°F)** The **portion of air actually cooled to coil temp** is: \[ 1 - BF = 1 - 0.08 = 0.92 \] So, the **amount of air at 57°F and 56°F bh** is: \[ \text{cfm}_{\text{leaving}} = \text{Total cfm} \times (1 - BF) \] \[ \text{cfm}_{\text{leaving}} = 2080 \times 0.92 = 1913.6\, \text{cfm} \] --- ## **Final Answer** ### **The amount of air that leaves the air conditioning unit at 57°F and 56°F bh is:** \[ \boxed{1914\ \text{cfm}} \] (**rounded to the nearest integer**) --- ### **Summary Table** | Parameter | Value | |----------------------|----------------| | Mixed Airflow | 2080 cfm | | Mixed Air Temp | 80.1°F | | Coil Surface Temp | 55°F | | Leaving Air Temp | 57°F | | Bypass Factor | 0.08 | | Leaving Air at 57°F | 1914 cfm | Let me know if you need the psychrometric chart or further clarifications!