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Let's see if I can remember this. Like Frank, I'm not sure what you're asking because it doesn't have much to do with the intake of a fan. But if you want to measure the Venturi effect, here's how:
In any fluid stream, there are two pressures present. The velocity pressure is the pressure exerted by the flowing mass in the direction of flow but it can't be measured alone. The second pressure is the static pressure which acts in all directions, and is the pressure that is exerted by the fluid on the walls of the duct or pipe.
The measurements need to be taken in a long enough section of tube or duct so that the flow stream is smooth, not turbulent. (Near the intake of a fan you will get interesting results but not because of the Venturi effect.)
If a sensing tube is placed in the stream parallel to the flow with an opening facing upstream, this probe will register the total pressure of the system, both velocity pressure and static pressure.
If another probe is inserted at right angles to the flow, this will register only the static pressure.
If the two probes are connected to a device (a manometer) so that the pressures oppose one another, the effect is to subtract the static pressure from the total pressure picked up by the first probe and the resultant reading gives the velocity pressure.
Now, as the cross sectional area of the duct or pipe is gradually narrowed and then gradually enlarged again to create a venturi, the same two measurements are taken within the restricted portion, and compared to the original readings. It will be discovered that the total pressure, picked up by the first probe is exactly the same in both sections, as Frank's formula shows.
The velocity pressure will have increased proportional to the increase in velocity and the static pressure will be found to have decreased by the same amount. This is the Venturi effect.
Of course, you can just measure the change in static pressure in the two sections, but the principle at work is of constant total pressure while changing the ratio of velocity pressure to static pressure.
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