# Repeat all parts of Problem 15.D12 but with a water rate of (q=0.000015 mathrm{~m}^{2} / mathrm{s}). Problem

## Question:

Repeat all parts of Problem 15.D12 but with a water rate of \(q=0.000015 \mathrm{~m}^{2} / \mathrm{s}\).

**Problem 15.D12**

Water at \(20^{\circ} \mathrm{C}\) is flowing down a \(3.0 \mathrm{~m}\) long vertical plate at a volumetric flow rate per meter of plate width of \(q=0.000005 \mathrm{~m}^{2} / \mathrm{s}\). Entering \((y=0)\) water is pure. The water is in contact with carbon dioxide gas that is saturated with water vapor at \(20^{\circ} \mathrm{C}\) (no water is evaporating). Carbon dioxide transfers into the water. At the water-gas surface \((\mathrm{z}=0)\), water and carbon dioxide are in equilibrium at the solubility limit of carbon dioxide at \(\mathrm{C}_{\mathrm{CO} 2 \text {,surf }}\). Estimate Fickian infinite dilution diffusivity by adjusting the value from Table 15-3 for the temperature difference by assuming that \(\mathrm{E}_{\mathrm{o}}=2000\) \(\mathrm{cal} / \mathrm{mol}\) in Eq. \((15-22 \mathrm{c})\). At \(20^{\circ} \mathrm{C}\), the solubility of carbon dioxide in water is \(1.7 \mathrm{~g} / \mathrm{kg}\) water.

**a.** Determine film thickness \(\delta\), average vertical velocity of film, and Reynolds number.

**b.** Is flow laminar? If no surfactant is added, do you expect ripples on the surface? If surfactant is added, do you expect ripples on the surface?

**c.** With no surfactant, determine average mass transfer coefficient and average Sherwood number.

**d.** Per meter of plate width, at what rate \((\mathrm{kg} / \mathrm{s})\) is carbon dioxide transferred into water over the length of the plate?

**Equation 15-22c**

## Step by Step Answer:

**Related Book For**

## Separation Process Engineering Includes Mass Transfer Analysis

**ISBN:** 9780137468041

5th Edition

**Authors:** Phillip Wankat