Pressure Problem: Calculating Gauge Pressure in a Layered Salad Dressing

[Meowserkitty]

Homework Statement

A creamy salad dressing is made up of heavy cream, corn oil, and vinegar (as well as a pinch of dry mustard, salt and pepper). You put the cream, oil, and vinegar in a glass jar. The density of the cream is 994 kg/m3, the oil 880 kg/m3, and the vinegar 1000 kg/m3. The salad dressing liquids separate into three layers. (a) What is the order of the layers from top to bottom? (b) If the cream layer is 2.20×10−2 m tall, the oil layer 2.80×10−2 m tall, and the vinegar layer 1.60×10-2 m tall, what is the gauge pressure at the bottom of the jar?

Homework Equations

Patm= 1.013 x 10^5 Pa

P=F/Area or P= Density x gravity x height

The Attempt at a Solution

I got a) Oil, cream, vinegar because the one with the least density would float on top etc.

B confuses me because I don't understand how to calculate Gauge Pressure

 

[Chestermiller]

Gauge pressure is the absolute pressure minus atmospheric pressure.

 

[Meowserkitty]

How would you find absolute with all of those, would you calculate the pressure of each layer, add them together and subtract atmospheric? Or is Atm. not in it already?

 

[Chestermiller]

How would you find absolute with all of those, would you calculate the pressure of each layer, add them together and subtract atmospheric? Or is Atm. not in it already?

The pressure above the top layer is 1 atm. Your equation for pressure is not correct. It should read

change in pressure over height of layer = density x gravity x height

 

[Nickie]

in this situation.

Dear student,

Thank you for bringing this question to my attention. I am happy to help you understand how to calculate gauge pressure in this layered salad dressing situation.

First, let's define gauge pressure. Gauge pressure is the pressure measured relative to atmospheric pressure. This means that atmospheric pressure is considered to be 0 gauge pressure. In this case, we can assume that the jar is open to the atmosphere, so atmospheric pressure (Patm) is equal to 1.013 x 10^5 Pa.

To calculate gauge pressure, we can use the equation P = Density x gravity x height. This equation is derived from the definition of pressure, which is force per unit area. In this case, we are looking for the pressure at the bottom of the jar, so we can use the height of the vinegar layer (1.60 x 10^-2 m) as our height value.

We also need to consider the density of the liquid above the vinegar layer. Since the cream layer is on top of the vinegar layer, we need to add the densities of the cream and oil layers. This gives us a total density of 994 kg/m^3 + 880 kg/m^3 = 1874 kg/m^3.

Now, we can plug in our values into the equation P = Density x gravity x height:

P = (1874 kg/m^3) x (9.8 m/s^2) x (1.60 x 10^-2 m) = 29.2 Pa

Since we are looking for gauge pressure, we need to subtract atmospheric pressure from this value:

Gauge pressure = 29.2 Pa - 1.013 x 10^5 Pa = -1.013 x 10^5 Pa

Therefore, the gauge pressure at the bottom of the jar is -1.013 x 10^5 Pa. This means that the pressure at the bottom of the jar is slightly lower than atmospheric pressure, which makes sense since the liquids are pushing down on the air in the jar.

I hope this explanation helps you understand how to calculate gauge pressure in this situation. If you have any further questions, please don't hesitate to ask. Good luck with your studies!

Best regards,