Republished with permission from Barista Hustle. View original post.
Does having flow restrictors in my machine mean I get the same flow rate regardless of where I have my pump pressure set to?
The short answer is: no. Flow and pressure are linked, so all other things being equal, increasing the pressure will increase the flow out of a restrictor. However, the physics around flow is complicated, especially when you start to factor in a coffee puck.
First, we need to understand what a flow restrictor does. A flow restrictor is a section of tube with a very small diameter (typically 0.8mm), placed somewhere between the pump and the group in an espresso machine. It looks like a blanking nut with a pinhole through it. The small diameter of a flow restrictor limits the flow, which increases the time it takes to wet the puck and fill the space above the puck (headspace), creating a small window of low pressure pre-infusion.
First, let’s take a look at a simplified schematic of the route water takes to reach the coffee:
The water entering the machine is pressurised by the pump, forcing it into the pipes connecting the pump to the flow restrictor. The pressure gauge is usually connected to the pipes here, meaning that it measures the pressure at the pump, rather than the pressure at the coffee puck itself. The flow restrictor lies between the pump and the group head, usually fairly close to the group itself. At the group head, the water must flow through small holes in the dispersion block and shower screen, pass through the headspace between the screen and the puck, and then finally through the puck itself.
Let’s consider the case when the pump is on, but no coffee is in the group. The pressure causes water to flow through the pipes towards the restrictor, building up the pressure in the pipework until it reaches the set pump pressure. Downstream of the restrictor, the water can flow easily out through the grouphead. This means that pressure can’t build up in the group, so we can effectively ignore what happens here in this case. Instead, the flow in the whole system is determined by the flow through the restrictor. (We’re ignoring the small bit of resistance created by the pipes themselves in this case)
The restrictor itself is a small tube, which means we can consider the flow of water through it to be laminar. This means that the water molecules pass through it in straight lines, rather than creating eddies that interfere with the flow. In laminar flow, the flow rate is directly proportional to the pressure gradient, which means if you double the pump pressure, you double the flow rate. So we can clearly see that the restrictor doesn’t give a constant flow, but it still varies with the pump pressure.
Turbulent flow happens when the water passes through a wider aperture — for instance in a dedicated brew boiler. In turbulent flow, the eddies interfere with the flow more as pressure increases, meaning that flow only increases with the square root of pressure. Nonetheless, an increase in pressure still means an increase in flow rate.
Once you factor in the puck, things become a little more complicated. Let’s consider the situation when the flow through the puck is very slow (close to zero). In this case, once the puck is wet and the headspace is full, the pressure at the group will build up to become more or less the same as the pressure at the pump. Because the water is passing through the restrictor more easily than through the puck, it no longer restricts the flow but instead, the flow through the whole system is determined by how quickly it moves through the puck. In this case, pressure can have unexpected effects on the flow rate, because of the effect of pressure on the puck itself. Increased pressure will increase the flow up to a certain point, but high pressure can press the coffee particles in the puck together, eliminating any gaps for water to flow through, and thus actually reduce the flow. (Rao 2013a)
A real life situation is somewhere in between these two scenarios. The pressure upstream of the restrictor will always be more or less pump pressure. At first, the puck creates strong resistance to water flow, allowing pressure to build up downstream of the restrictor, creating a situation similar to the second scenario above. As the pressure builds up in the group, the flow through the puck will increase up to a certain point, and in this scenario, the flow rate is determined by the makeup of the puck. However, as coffee solids start to dissolve, the puck begins to break down during the shot, providing less and less resistance (Rao 2013b). This means the flow rate through the puck will increase throughout the duration of the shot, until it approaches the same rate that you have with no coffee in the group at all. At this point, we’re back to the first scenario above, where the flow rate is exactly proportional to the pump pressure.
The interesting thing to note here is that even with steady pump pressure, the pressure at the puck is actually decreasing throughout the shot, yet the flow rate is increasing. This is one of the reasons that flow profiling, as opposed to pressure profiling, is so interesting – it can compensate for inconsistencies in the puck, especially as it starts to break down.
One final technical note: an espresso machine that uses a heat exchanger to heat the brewing water will often have additional flow restrictors in the heating loop. These don’t affect flow to the group when the pump is engaged, but instead control how quickly the water circulates through the heat exchanger, and therefore influence the brew temperature.
S Rao, 2013a. Chapter 3: Pump Pressure. In: Espresso Extraction: Measurement and Mastery
S Rao, 2013b. Chapter 11: Pressure Profiling. In: Espresso Extraction: Measurement and Mastery