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#### Published: يناير 31, 2019

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 القُرص.

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 القُرص and fill the space above the القُرص (مساحة الرأس), 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 القُرص 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 مساحة الرأس between the screen and the القُرص, and then finally through the القُرص 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 لضغط الضخ. 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 المقاومة 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 لضغط الضخ, 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 لضغط الضخ.

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 القُرص, things become a little more complicated. Let’s consider the situation when the flow through the القُرص is very slow (close to zero). In this case, once the القُرص is wet and the مساحة الرأس 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 القُرص, it no longer restricts the flow but instead, the flow through the whole system is determined by how quickly it moves through the القُرص. In this case, pressure can have unexpected effects on the flow rate, because of the effect of pressure on the القُرص itself. Increased pressure will increase the flow up to a certain point, but high pressure can press the coffee particles in the القُرص 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 لضغط الضخ. At first, the القُرص creates strong المقاومة 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 القُرص will increase up to a certain point, and in this scenario, the flow rate is determined by the makeup of the القُرص. However, as coffee solids start to dissolve، فإن القُرص begins to break down during the shot, providing less and less المقاومة (Rao 2013b). This means the flow rate through the القُرص 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 لضغط الضخ.

The interesting thing to note here is that even with steady لضغط الضخ, the pressure at the القُرص 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 القُرص, 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.

#### المراجع

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

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# 1 تعليق

1. The flowrate through the restrictor will always be the same unless there’s a coffee puck downstream creating more restriction. Flow rate out of the coffee bed will be zero until all the air has been exhausted from the basket and replaced with water, but the flow rate through the restrictor jet will determine how quickly that happens.
https://thammyxinh.vn/day-hoc-phun-xam-tham-my/

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