Lecture 15

# Lecture 15 - We learned 5.3.3 Flowrate measurement A note...

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1 5.3.3 Flowrate measurement: A note on stagnation point : in fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. If elevation effects are neglected, the stagnation pressure is the largest pressure obtainable along a given streamline. It represents the conversion of all of the kinetic energy into a pressure rise. P V P s 𝑃𝑃 + 1 2 𝜌𝜌𝑉𝑉 2 = 𝑃𝑃 𝑠𝑠 We learned…

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2 5.3.3 Flowrate measurement 5.3.3.1 Pitot or pitostatic tubes: Principle of operation: – At (1), the flow is undisturbed (V 1 = V) – At (2), the fluid is not flowing, stagnation point (V 2 = 0) Gives a point (local) velocity not an average velocity. If we apply the Bernoulli equation between points 1 and 2, using V 2 = 0 and assuming z 1 = z 2 , we find that: 𝑃𝑃 2 = 𝑃𝑃 1 + 1 2 𝜌𝜌𝑉𝑉 1 2 𝑉𝑉 = 2 𝑃𝑃 2 − 𝑃𝑃 1 𝜌𝜌 𝑃𝑃 1 = 𝑃𝑃 𝑎𝑎𝑎𝑎𝑎𝑎 + 𝜌𝜌𝜌𝜌𝜌 𝑃𝑃 2 = 𝑃𝑃 𝑎𝑎𝑎𝑎𝑎𝑎 + 𝜌𝜌𝜌𝜌𝜌𝜌 𝑉𝑉 = 2𝜌𝜌 𝜌𝜌 − 𝜌
3 5.3.3 Flowrate measurement 5.3.3.2 Venturi meters: Principle of operation: – At (1), the flow is undisturbed (V 1 = V) – At (2), the flow area is decreased (V 2 > V 1 ) Gives the average velocity in the pipe. An effective way to measure the flowrate through a pipe is to place some type of restriction within the pipe and to measure the pressure difference between the low-velocity, high-pressure upstream section (1) and the high-velocity, low-pressure downstream section (2).

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