You can determine a fluid’s pressure from its flow rate using the Bernoulli equation, if you know the pressure and flow rate at a different point in the fluid’s path of flow. The governing equation is P + (0.5)?V^2 + ?gh = a constant. Here, P stands for pressure, ? is the fluid’s density, V is its velocity, h is its height and g is the gravitational acceleration constant, which equals 9.80 meters per second-squared. The way to think of this intuitively is that the sum of the static pressure, the dynamic pressure and the gravitational pressure remains constant.
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Draw a diagram of the path of fluid flow for which you want to calculate the flow rate. Suppose that at the location in the fluid’s path where you want to know the pressure, you already know the velocity, density and altitude. Denote them V_1, ?_1 and h_1. Suppose also that you know all three plus the pressure at some other location in the fluid’s path. Denote them V_2, ?_2, h_2 and P_2.
Calculate the constant mentioned in the introduction, using the data at point 2. Denote it with the letter C. In other words, calculate C = P_2 + (0.5)?_2 x (V_2)^2 + ?_2 x g x h_2.
For example, suppose you know the velocity and pressure at another point that is the same level as the point where you’re trying to find the flow rate. Then you can set h_1=h_2=0 without loss of generality. Suppose also that no compression is going on, so ?_1=?_2. If P_2= 1000 Pascals (pressure of standing water 4 inches deep), V_2= 1.0m/s and ?_2 = 1000kg/m^3, then C = 1,500 Pascals (Pa).
Calculate C - (0.5)?_1 x (V_1)^2 - ?_1 x g x h_1. This equals P_1, the pressure at the point where you knew the flow rate V_1.
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