To solve for the unknown existing data using Kern's method for the heat exchanger, we'll follow a structured approach. However, some necessary assumptions or additional data may be required, particularly fluid properties or flow rates, which are not directly available from the image provided. Let's proceed with the given data and make some standard assumptions where necessary.

Step 1: Calculate Baffle Spacing (B)

The baffle spacing can be calculated using the formula:

$B = \frac{L}{N_b + 1}$

For the existing data:

• Tube Length $L = 0.380 \, \text{m}$
• Number of Baffles $N_b = 21$

$B = \frac{0.380 \, \text{m}}{21 + 1} = \frac{0.380}{22} \approx 0.01727 \, \text{m}$

Step 2: Shell-Side Heat Transfer Coefficient (h_s)

The overall heat transfer coefficient $U$ for clean conditions is given by:

$\frac{1}{U_c} = \frac{1}{h_s} + \frac{1}{h_t} + \text{fouling factors}$

Without explicit data for tube-side heat transfer coefficient $h_t$, fouling factors, and fluid properties, we assume that $h_t$ and fouling factors are constant between the calculated and existing setups. This allows us to compare the ratio:

$\frac{h_s(\text{existing})}{h_s(\text{calculated})} = \frac{U_c(\text{existing})}{U_c(\text{calculated})}$

Given:

• $U_c(\text{calculated}) = 376.85 \, \text{W/m}^2\text{K}$
• Assume $U_c(\text{existing})$ is similar as $U_f(\text{calculated}) = 364.49 \, \text{W/m}^2\text{K}$.

For simplification: $h_s(\text{existing}) \approx h_s(\text{calculated}) = U_c(\text{calculated})$

We assume that: $h_s(\text{existing}) \approx 376.85 \, \text{W/m}^2\text{K}$

Step 3: Pressure Drop Calculations

Tube Side Pressure Drop $\Delta P_t$

For the tube-side pressure drop, Kern’s method gives:

$\Delta P_t = f_t \times \frac{G_t^2 \times L}{2 \times D_t \times \rho}$

Given the complexity and the lack of specific tube-side data, this step typically requires:

• $f_t$ (friction factor)
• $G_t$ (mass velocity)
• $D_t$ (tube diameter)
• $\rho$ (density of the fluid)

Since the calculated value is $0.00134 \, \text{kgf/cm}^2$, we assume this approximates well with the existing conditions due to the similarity in design. Thus, the existing data value would be close to this value.

Summary of Results:

1. Baffle Spacing (B) for existing: $B = 0.01727 \, \text{m}$
2. Shell-Side Heat Transfer Coefficient for existing: $h_s \approx 376.85 \, \text{W/m}^2\text{K}$
3. Tube-Side Pressure Drop (ΔPt) for existing: $\Delta P_t \approx 0.00134 \, \text{kgf/cm}^2$

Final Notes:

This solution is based on the provided data and assumptions due to missing information such as fluid properties and detailed dimensions of the heat exchanger. For exact results, more precise data is needed.

Would you like to refine any of these calculations or need further assistance on a particular aspect?

Follow-up Questions:

1. Would you like to validate the shell-side heat transfer coefficient with more detailed fluid properties?
2. Should we delve deeper into the tube-side pressure drop calculation using additional assumptions?
3. Would you like to explore fouling factor determination based on the provided heat transfer coefficients?
4. Is there a need to calculate the heat exchanger area based on the tube count?
5. Do you have specific fluid data that can refine these results?

Tip:

Always cross-check your results with empirical correlations or data from similar heat exchangers to ensure the validity of your calculations.