Help Solve Breathing Homework Problem | Jet Nebulizer

[celtchic]

I really want to thank everyone for the help you've given me. I have another question that I need help with. Here goes:

I do not know how to work this problem…can anyone help?

A common means of delivering medication to the lungs is a “Jet Nebulizer”. A simplified diagram of a nebulizer is shown here – medicine is placed in a cup, air is passed through a “venturi tube”, and the resulting pressure difference drives fluid-borne medicine from the cup into the air stream where it is dispersed into a vapor to be inhaled into the lungs. (Incidentally, this same principle is behind the operation of a carburetor in a gasoline engine.)

(1) A patient needs medicine that has a density of 1.25% that of water. The dimensions of the nebulizer (see below) are height medicine cup = 6 cm diameter venturi tube= 1 cm

What minimum flow of air (RVol) must pass through the venturi tube in order to bring the medicine into the air stream, even if the cup is nearly empty? Give your answer in cm3/sec.

A: I know that I will use either of these two eqations but I really do not how to solve these equations in either one…..

A1V1=A2V2=Rvol


P1 + pgy1 + ½rv12= P2 + pgy2 + ½pv22

Thanks for the help in adavance!

 

[97nismo]

did you figure this one out? I have a simular proplem and I was wondering how you worked this out? Anybody got any suggestions?

Thanks

 

[M98Ranger]

First of all, I'm glad to hear that you received helpful responses for your previous question. Now, let's tackle this new problem together.

To solve this problem, we will use the Bernoulli's equation, which is the second equation you mentioned. It states that the total energy of a fluid remains constant along a streamline. In simpler terms, it means that the sum of the pressure, potential energy, and kinetic energy at one point in the fluid must be equal to the sum of those three at any other point in the fluid.

In this case, we will use the Bernoulli's equation to find the velocity of the air passing through the venturi tube. We know that the pressure at the top of the cup (P1) is equal to the atmospheric pressure, and the pressure at the venturi tube (P2) is equal to the atmospheric pressure plus the pressure difference caused by the air flow through the tube. We also know that the potential energy (pgy) is the same at both points since they are at the same height. Therefore, we can ignore those terms in the equation.

Now, to find the kinetic energy (1/2rv^2), we need to know the density of air (r) and the velocity (v). The density of air is approximately 1.225 kg/m^3, and we can find the velocity by rearranging the first equation you mentioned:

A1V1 = A2V2

V2 = (A1/A2) x V1

Since we are given the dimensions of the nebulizer, we can calculate the areas A1 and A2. The area of the medicine cup is equal to the area of a circle with a diameter of 1 cm, which is 0.785 cm^2. The area of the venturi tube is equal to the area of a circle with a diameter of 6 cm, which is 28.3 cm^2.

Now, we can plug in the values into our equation:

V2 = (28.3/0.785) x V1 = 36.06 x V1

Next, we can plug in the values into the Bernoulli's equation:

P1 + ½rv1^2 = P2 + ½rv2^2

0.5 x 1.225 x V1^2 = 0.5 x 1.