Mass balance (material balance)
Matter does not appear or vanish in a normal chemical plant. So we can count it, like money. Draw a box around the tank or machine. This box is called the system. Every pipe that crosses the box is a stream.
The rule is: mass in = mass out + mass stored. The stored part is also called accumulation. If the level in the tank does not change, nothing is stored. We call this steady state, and then mass in = mass out.
You can balance the total mass, and also each substance alone, like salt or sugar in a mix. A reaction can turn one substance into another, but the total mass still stays the same.
Mixing streams: a salt example
Mix 60 kg of 10 % salt water with 40 kg of 30 % salt water. Total in = 100 kg, so total out = 100 kg. Salt in = 0.10 × 60 + 0.30 × 40 = 6 + 12 = 18 kg. All of it leaves in the 100 kg, so the outlet is 18 % salt. Total balance first, then the balance of each substance.
Energy balance
Energy is also never lost. It only moves or changes form. The rule is: energy in = energy out + energy stored. In a heated tank, energy comes in as heat from the heater. It leaves with the hot product and as small losses to the air.
To heat a flowing liquid, use Q = m × c × ΔT. Here m is the mass flow (kg/s), c is the specific heat (water: 4.2 kJ per kg per °C) and ΔT is the rise in temperature. If m is in kg/s and c in kJ/(kg·°C), Q comes out in kJ/s, which is kW.
Unit conversion
A balance only works if all numbers use the same units. Convert first, then calculate. Use SI units where you can.
- 1 h = 3600 s, and 1 min = 60 s
- 1 m³ = 1000 L
- 1 t (tonne) = 1000 kg
- 1 kW = 1 kJ/s, and 1 MW = 1000 kW
Example: 3.6 m³/h = 3600 L/h = 60 L/min = 1 L/s. A trick: write the unit with every number and cancel like fractions.
Try it
In the 3D: first guess, then check. Set A = 70, B = 30 and Out = 80. Guess if the level will rise or fall. Then read the box under the tank. At home: fill a bucket with a mug while a small hole leaks. Count mugs in and mugs out in one minute. Does the water level match In - Out?
Key formulas and definitions
- Mass in = mass out + mass stored
- Stored = In - Out (steady state: stored = 0)
- Energy in = energy out + energy stored
- Q = m × c × ΔT (Q in kW if m in kg/s, c in kJ/kg·°C)
- 1 kW = 1 kJ/s; 1 m³ = 1000 L; 1 h = 3600 s
Worked examples
1. Feed is 100 kg/min and the outlet is 80 kg/min. How much is stored every minute?
Stored = In - Out = 100 - 80 = 20 kg/min. The level rises.
2. Mix 60 kg of 10 % salt water with 40 kg of 35 % salt water. Find the salt percent of the mixture.
Salt = 0.10 × 60 + 0.35 × 40 = 6 + 14 = 20 kg. Total = 100 kg. So the mixture is 20 % salt.
3. Change 3.6 m³/h into L/min.
3.6 m³ = 3600 L. 3600 L/h ÷ 60 = 60 L/min.
4. Water flows at 2 kg/s and is heated from 20 °C to 50 °C. How much heat is needed? (c = 4.2 kJ/kg·°C)
Q = m c ΔT = 2 × 4.2 × 30 = 252 kJ/s = 252 kW.
5. An empty 600 L tank gets 150 L/min and loses 90 L/min. When is it full?
Net = 150 - 90 = 60 L/min. Time = 600 ÷ 60 = 10 minutes.
6. A 420 kW heater warms 2 kg/s of water at 20 °C in steady state. Find the outlet temperature.
ΔT = Q ÷ (m c) = 420 ÷ (2 × 4.2) = 50 °C. Outlet = 20 + 50 = 70 °C.
Common mistakes
- Mixing units, like kg/min with kg/h, in one equation. Convert first.
- Forgetting the stored part when the level is changing.
- Adding percentages instead of masses. Change % to kg first.
- Using Q = m c ΔT with m in kg/min but c in kJ per kg and expecting kW. Use kg/s.