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How does a Venturi Injector comply with energy conservation?

Venturi Injector

When the water flow enters the narrower cross section its velocity increases and its pressure decreases. When the pressure gets lower than ambient atmospheric pressure the atmosphere is pushing air or liquid through the injection tube into the main line.

The particles in the injection tube get accelerated. Following conservation of energy, where does the kinetic energy come from? Please notice that I am not asking whether the kinetic energy of the flow at the exit is equal to the entry (it is not because of inelastic losses in the mixing process), but: when a fluid is pushed or sucked in from the side, where does the energy come from to accelerate it?

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Conservation of energy is exactly how the venturi effect arises. In an incompressible fluid, conservation of energy states that $E = E_k + E_{p,pressure} + E_{p,gravity} = \frac{1}{2} mv^2 + PV + mgz = constant$
by dividing each term with volume, it becomes the Bernoulli Principle:
$\frac{1}{2} \rho v^2 + P_{static} + \rho gz = anotherConstant$

So, how does this process happen? The molecules which originally move equally much in every direction becomes redirected to flow forward(and hence flow more quickly although the speed of molecules remain the same), thus colliding with the wall less strongly, reducing the static pressure in the neck. In the end, the total energy of the fluid has not been changed, it is only that the molecules' movement has been redirected to another direction, and thus some internal kinetic energy(random movement) is converted into "external" kinetic energy(organized flow), though the sum has not changed at all.

The same is said to the fluid sucked into the venturi: originally random movement of molecule contributes strictly to the internal energy. When the pressure at one side is reduced, a portion of the randomly moving molecules will be able to get out because of their direction. This getting out is when the internal energy is converted to "external" kinetic energy.

In a nutshell, the venturi effect redirects molecules to convert their internal kinetic energy to "external" kinetic energy in order to make them move without energy input.

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  • $\begingroup$ That's an interesting answer. But when internal kinetic energy is converted to "external" kinetic energy, isn't that contrary to the second law of thermodynamics? $\endgroup$
    – Chris
    Jul 5 '15 at 10:46
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The answer comes from the difference in pressure between the middle and the start of the flow. Since there is a decrease in pressure (= Force/area) it means that there is an overall force pushing the liquid forward, which does work, accelerating the liquid.

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