I am currently building a brake system for a vehicle ground up and I know that the diameter of the master cylinder would affect the braking force proportionally to the area of the master cylinder. But I was wondering if the diameter of the brake line would affect the braking pressure? I'm trying to be very precise with the braking force that's being delivered


Edit: If it does matter does anyone know what math formula I could use to determine the fluid pressure

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    Diameter of pipe won’t affect the pressure unless it is so small that velocity losses become significant. As for a formula, check out Bernoulli. – Solar Mike Dec 8 '20 at 7:09

According to Pascal's law, pressure must everywhere be equal. Pressure is defined as a force on a surface. Pressure equals force devided by area P = F / a. That is, the area of the master and slave cylinders (those inside the calipers or brake drums). So, brake pressure is only affected by the area of the master- and slave cylinders and the force that's applied to the brake pedal. This answers the question, but here is some more information:

Since P = F / a, F = P . a. If you have a master cylinder with a surface area of 10 cm^2, and you have a caliper with two 25cm^2 pistons, the total surface area in the caliper pistons is 5x greater, thus the force applied to the brake disk is multiplied by 5.

In practice, brake force is mulitplied even further because of mechanical advantage. The brake pedal (or brake lever on a motorcycle) provides leverage. Also vacuum powered brake boosters are used to create more pressure.

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