In a cross-flow filtration process, the pressure drop (AP) driving the fluid flow is 2 atm,
inlet feed pressure (Pi) is 3 atm and filtrate pressure (Pf) is equal to atmospheric pressure.
The average transmembrane pressure drop (4Pm) is _
atm.
Official Answer Key:
1 to 1
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.63)**
**1. Governing Concept & Definition**:
- **Topic**: Bioprocess Separation & Cross-Flow Membrane Filtration
- Transmembrane pressure drop ($\Delta P_{\text{TMP}}$) is:
$\Delta P_{\text{TMP}} = \frac{P_{\text{in}} + P_{\text{out}}}{2} - P_{\text{permeate}}$
**2. Detailed Step-by-Step Calculation**:
- Given the system pressure boundary conditions where $\Delta P_{\text{channel}} = P_{\text{in}} - P_{\text{out}} = 2\text{ atm}$, solving for the permeate pressure yields 1 atm.
**3. Final Answer**:
- **Calculated Value**: **1 atm**
- **Official GATE Accepted Range**: **1 to 1**
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