# Is the density of water EVER changed by pressure?

• ph7ryan
In summary, the student received a lower score on their fluid mechanics quiz due to making incorrect assumptions and not reading the problem carefully. They argued that their answer was correct, but their understanding of the problem was flawed and they were marked off for it. The student also questioned if there were any scenarios where the density of water could change due to pressure, but ultimately accepted their mistake and planned to do better on future quizzes and exams.
ph7ryan
We just got our fluid mechanics quizzes back today and I was unpleasantly surprised with a 13/20 when I was expecting close to a perfect score.

I was counted off a full 6 points (30%) for essentially using the wrong variable because in my rushed state I didn't read the problem carefully enough...

Basically the problem had a picture of an intake plenum from what would be on your typical 4 cylinder car. It mentioned that water (that's the problem, I was assuming that AIR would be going through an AIR plenum) was going in at the inlet point 1, and exiting at points 2,3,4,and 5 at rates that decreased by .85 from each outlet forward (ie, mfr3=(.85)mfr2, mfr4=(.85)mfr3, etc.). We were to find the flowrate at port 1 (ie point 2).

My problem, is that I wrote the assumption that the cross sectional areas A2=A3=A4=A5, and because I was rushed at this problem, I put V2=V3=V4=V5. The TA circled both of these, and put an x by each one and counted off a total of 6 points for the problem because I solved it by using density (rho) of each port rather than the mass flow rate (m dot).

EVEN THOUGH, I got the right answer, he counted off more than people who simply divided the inlet mfr by 4 (ie 12.5 kg/s). They only got 4 counted off. When I went to talk to him he was pretty stern about not changing the grade, because the problem states WATER rather than air, and density wouldn't change (incompressible).

My question is this:
Is there ever, even in extreme circumstances, any time where density of water could change because of pressure. Because I could then make the argument that velocity COULD be constant, and density WOULD change (based on the fact that mfr is a function of density and velocity). Nevermind the fact that I could have used a smiley face to represent whatever was being calculated because a variable is simply a value holder, and I had the concept right, I think it is a little ridiculous that I get counted off MORE than the people who got the problem completely wrong, but I will need a scenario to essentially prove my way to be right (which it would have if it was AIR going through and AIR plenum, but that's beside the point.)

Thanks for any help.

Unless I'm misunderstanding what you did, I don't see how you can possibly defend your answer as correct. If the areas are equal, the velocities will not be even close to equal, due to the differing mass flow rates.

cjl said:
Unless I'm misunderstanding what you did, I don't see how you can possibly defend your answer as correct. If the areas are equal, the velocities will not be even close to equal, due to the differing mass flow rates.

Well because mass flow rate is a product of density and velocity, if one is constant, the other would encounter all the change. So basically I made the "assumption" to hold velocity constant and calculate completely using density. If it wasn't right I wouldn't have gotten the right answer. I'm not asking for full credit, but it's retarded that I get less credit than if I wouldn't have even done it.

ph7ryan said:
Well because mass flow rate is a product of density and velocity, if one is constant, the other would encounter all the change. So basically I made the "assumption" to hold velocity constant and calculate completely using density. If it wasn't right I wouldn't have gotten the right answer. I'm not asking for full credit, but it's retarded that I get less credit than if I wouldn't have even done it.

Yes, but even with air, that assumption is completely incorrect. I would expect anyone taking a fluid mechanics course or quiz to know that, unless it was at a high school level or below. If the velocities in question are below mach 0.3 or so (~100m/s for air at standard conditions), I would treat it as incompressible, and above that, it gets complicated (both density and velocity would change significantly). What level and type of course is this for, out of curiosity? I would expect perhaps a bit of lenience if this were a fluid mechanics unit in a freshman physics course, for example, but not in a dedicated fluid mechanics course.

The density of water changes very little with pressure. Look up the bulk compressibility of water. To change the density by 0.1% requires a pressure of 2.2 MPa. So for the system you are looking at, the density is virtually constant.

Chet

ph7ryan said:
Well because mass flow rate is a product of density and velocity, if one is constant, the other would encounter all the change. So basically I made the "assumption" to hold velocity constant and calculate completely using density. If it wasn't right I wouldn't have gotten the right answer. I'm not asking for full credit, but it's retarded that I get less credit than if I wouldn't have even done it.

How you arrive at your answer is just as important as the answer at which you arrive. If you did get the right answer here, it was clearly purely by luck and your understanding of the problem was fundamentally flawed. For that you should get marked off pretty substantially. If you used that same logic in another problem you would indubitably get it completely wrong.

Water being "incompressible" is a fundamental assumption that holds in nearly all practical flows, so the fact that you treated a problem using water as not only compressible, but as a situation where the density was really the only thing changing, is completely wrong. Even taking into account the fact that you performed the problem assuming air was the working fluid the assumptions you made were completely incorrect and have no justification in physics.

You need to just take this maturely and move on. Learn the problems with your logic and fix it for the next quiz and exam. Your position is indefensible, and continuing to argue with the grader or the professor is just going to tempt them to be more harsh with you in the future.

The teacher was testing you for being able to spot a curveball.

## 1. What is the relationship between pressure and the density of water?

As pressure increases, the density of water also increases. This is because pressure compresses the molecules of water together, making them occupy less space, thus increasing the density.

## 2. How does the density of water change with depth?

The density of water increases with depth due to the increase in pressure. At the surface, the density of water is 1 gram per cubic centimeter, but at the bottom of the ocean, it can reach up to 1.03 grams per cubic centimeter.

## 3. Is there a limit to how much the density of water can change with pressure?

Yes, there is a limit. Water is considered to be an incompressible substance, meaning that it cannot be compressed infinitely. Therefore, there is a limit to how much the density of water can change with pressure.

## 4. Does temperature also affect the density of water under pressure?

Yes, temperature has an impact on the density of water under pressure. As temperature increases, the molecules of water gain more energy and move faster, causing them to take up more space and decrease the density. However, pressure still remains the dominant factor in changing the density of water.

## 5. Can the density of water decrease under high pressure?

No, the density of water cannot decrease under high pressure. As discussed earlier, water is considered an incompressible substance, so even under high pressure, the density will continue to increase. Only at extreme pressures, such as those found in the core of a planet, can the density of water decrease.

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