# 1.1 The art of balancing: examples

Course subject(s) 1. Balance Equation: our working horse

### Examples

A variety of different exercises are set as an example for you to look at in every learning step. Feel free to first try the example yourself and then watch the video, or do so the other way around. Whatever works best for you!

The presented questions have different levels:

• The elementary questions should be easy to follow and solve.
• The medium questions can be a little tricky in some cases. Don’t worry if you don’t get them correct after your first attempt.
• The advanced ones are there to challenge you and for more advanced learners.

Please watch the video below for a short introduction about the glass plate examples.

## An introduction to glass plate examples

Subtitles (captions) in other languages than provided can be viewed at YouTube. Select your language in the CC-button of YouTube.

## EXAMPLE 1.1A: FILLING A GLASS (ELEMENTARY)

This exercise shows how you can apply the mass balance to calculate how long it takes to fill a glass. The objective of this example is for you to learn about how to apply this to a randomly chosen volume scenario.

Consider a cylindrical volume with a height of 20 cm and a diameter of 5 cm. The volume is empty.

At a certain moment, we start to fill the glass with a volume flow rate of 20 mL per second. How long does it take before 80% of the volume is filled? The density of the fluid is 1000 kg/m3.

## Example 1.1A: Filling a glass (elementary)

Subtitles (captions) in other languages than provided can be viewed at YouTube. Select your language in the CC-button of YouTube.

In a laboratory, a micro-organism is grown under steady-state conditions on a certain substrate in a stirred tank reactor.

The liquid volume V = 1.25 L is constant.

The volume flow rate of the inlet is 0.10 L/h and contains 10 g/L substrate and no biomass.

The broth leaving the reactor has a flow rate of 0.13 L/h and contains 4.0 g/L substrate and 2.0 g/L biomass.

The difference in the volume flow rate at the entrance and the outlet is due to the addition of an alkali solution, needed to maintain the pH.

Set up the mass balances of substrate and biomass over the tank reactor and calculate the conversion rates of the biomass Rb and substrate rate Rs

Subtitles (captions) in other languages than provided can be viewed at YouTube. Select your language in the CC-button of YouTube.

## BONUS: EXAMPLE 1.1D: STEADY-STATE MASS BALANCE (MEDIUM)

Let’s consider a vessel where a certain mass flow rate of an aqueous salt solution (cs,in= 1.0 g/L) enters a well-defined volume and the same amount leaves the volume. Initially, the volume was filled with a salt solution with a concentration of 5 g/L water. The vessel is well mixed by a stirrer.

What is the steady-state concentration in the vessel, if the volume flow rate is equal to 10 L/s and the volume of the vessel is 100 L?