Bernoullis Equation for Fluid Flow Measurement

Several important types of fluid-flow-measuring devices are based on the frictionless form of Bernoulli s equation. Where the friction effects in these devices become significant, they are normally accounted for by introducing empirical coefficients and retaining the frictionless form of Bernoulli s equation, rather than by introducing the friction term into Bernoulli s equation. Thus, it seems appropriate to take up these devices before we discuss the friction term in Bernoulli s equation, even though these devices obviously involve some friction. 

The simplest pitot tube (invented by H. Pitot) is sketched in Fig. 5.6. This is sometimes called an impact tube or stagnation tube. It consists of a bent, transparent tube with one vertical leg projecting out of the flow and another leg pointing directly upstream in the flow. 

At location 1 the flow is practically undisturbed by the presence of the tube and hence has the velocity which would exist at location 2 if the tube were not present. At location 2, the flow has been completely stopped by the tube which has been inserted, so V2 = 0. Writing Bernoulli s equation between locations 1 and 2 yields 

But inside the pitot tube the fluid is not moving, so the pressure at location 2 is given by 

If all the fluid flow is in the horizontal direction, then the basic equation of 

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