Material Balance: Worked Examples

1. Calculator Inputs

At steady state, mix a 1,000 lb/h feed containing 90 wt% water with a 500 lb/h feed containing 20 wt% water. The remainder of each feed is ethanol. Find the total product flow and its mass composition.

On the calculator, select Mixing to load these exact inputs, then select Calculate balance. The unknown stream’s flow and composition fields are disabled because the calculator solves them.

2. Work through the component balances

Draw the boundary around the mixer. Assume no reaction, no accumulation, and no leaks or evaporation. Each component entering must leave at the same rate.

Total product flow

Water balance

Ethanol balance

Check closure

Do not average the inlet percentages directly. (90% + 20%)/2 = 55% would only apply to equal feed mass rates. This example needs a flow-weighted average.

3. Compare your answers

Live calculator check, October 19, 2026: the output is 1,500 lb/h at 66.7% water and 33.3% ethanol, with all component residuals zero. For a hand check, allow 0.001 lb/h in rates and 0.001 percentage point in composition.

Try check mode

Choose Check entered streams (no unknown), enter a product rate of 1,500 lb/h and product percentages of 66.666667 and 33.333333, and calculate. Small residuals around 0.000005 lb/h come from rounding; they are below the calculator’s closure tolerance.

Catch an incorrect composition: enter the same product rate but 55% water and 45% ethanol. The overall residual is still zero, but water has a +175 lb/h residual and ethanol has a −175 lb/h residual. The component balance fails.

4. Assumptions and scope

The fractions in this example are mass fractions. The same component-conservation structure works for nonreactive molar balances, but switching to mole basis does not convert mass fractions into mole fractions. Molecular weights would be required for that conversion.

This calculator solves one complete unknown stream, or checks all entered streams. It does not simultaneously solve multiple unknown outlet rates from specified compositions. The additional examples below show an unknown inlet and a two-outlet problem that needs algebra first.

Mixing can affect temperature, density and total volume. This mass balance does not model those effects, liquid-volume additivity, equipment size or physical separation performance. The exact arithmetic above was independently checked and then verified in the live calculator.

Additional example: Diluting a caustic solution to 15 wt%

Problem: You have 1,200 lb/h of a 35 wt% sodium hydroxide solution. How much pure water is needed to make a 15 wt% sodium hydroxide solution? Assume steady state, no evaporation, no leaks, and complete mixing.

Step 1: Balance the sodium hydroxide

Water added contains no NaOH, so all 420 lb/h of NaOH leaves in the diluted product.

Step 2: Calculate the diluted product flow

Step 3: Find the additional water

Answer: Add 1,600 lb/h of water. The outlet will be 2,800 lb/h at 15 wt% NaOH, assuming no losses.

Check in the calculator

1. Choose a mass basis and lb/h.
2. Create two components: NaOH and Water.
3. Add an inlet at 1,200 lb/h with 35% NaOH and 65% water.
4. Add an unknown inlet named Make-up water.
5. Add the known outlet at 2,800 lb/h with 15% NaOH and 85% water.
6. Solve for the make-up water inlet. It should return 1,600 lb/h at 100% water.

The calculation determines rates only. It does not account for heat of dilution, concentration-dependent density, temperature change, or compatibility of the mixing system. Caustic dilution can release substantial heat; address this separately in equipment design.

Additional example: Separating a slurry into product and reject

Problem: A separator receives 2,000 lb/h of slurry containing 12 wt% dry solids. The concentrated product contains 40 wt% solids and the reject contains 2 wt% solids. Estimate the flow rate of each outlet, assuming the solids are conserved and the stated compositions are achievable.

Step 1: Write an overall balance

Step 2: Write a solids balance

Step 3: Substitute and solve

Answer: About 526.3 lb/h concentrate and 1,473.7 lb/h reject. The solids split sums to 240 lb/h on both sides.

Check in the calculator

This problem initially has two unknown outlet flows. Solve the two simultaneous equations above first, then enter both calculated outlets in Check entered streams mode. Do not attempt to solve both unknown streams with the calculator's current single-unknown feature.

The mass balance does not predict whether the separator can actually achieve 40 wt% and 2 wt% solids. That requires separation performance or equipment data.

Which assumptions matter?

• Steady state: material in the equipment is not accumulating or decreasing over time.
• Nonreactive: no component is generated or consumed by chemical reaction.
• Consistent basis: weight fractions go with mass flow; mole fractions go with molar flow.
• Known compositions: every stream's fractions must total 100%.
• Process boundary: evaporation, venting, purge, leaks, and side draws count as outlet streams if they cross the boundary.

Mass balance or heat duty?

Use a material balance to find how much material goes into or out of a process. For heating, cooling, phase change, or heat of mixing, use a separate energy balance. See the Heat Duty Calculator.

Further reading

For the underlying conservation equations and degree of freedom analysis, see LearnChemE's material balances module and Colorado State University's introduction to material balances.

Common questions

These are illustrative steady state, nonreactive calculations, not validated separator or mixing equipment designs.

Keep checking

Browse all worked examples or choose the right pipe calculator.