Fluid Flow rate and fluid dynamics

[LiamB]

Homework Statement

More a report question but unsure where to put it.
Take a 5mL syringe and a 10mL syringe (both filled to 5mL) with the plungers removed.
Time how long it take to full drain each syringe
Make a statement regarding your results.

Homework Equations

Fluid flow rate = volume / time

The Attempt at a Solution

5mL fluid flow rate = 5x10-6 m3 / 3.48s = 1.44x10-6 m3/s
10mL Fluid flow rate = 5x10-6 m3 / 4.09s = 1.22x10-6 m3/s

Both syringes have an outlet diameter of 2mm however the 10mL syringe has a larger diameter in the reservoir. The results I was expecting were that the 10mL syringe would drain quicker.
I clearly did not get that and I so have been trying to work out why.
Am I on the right path by discussing how the fluid height to 5mL in the 10mL syringe is smaller due to the increased diameter?
I thought the increased surface area would mean an increased downward force on the water but my results simply disagree.

 

[Chestermiller]

How many replications did you do of each test?

 

[LiamB]

I ran it through 3 times each then calculated the average time.
for the 5mL syringe, 3.51s, 3.44s, 3.50s. for 10mL syringe I had 4.09s, 4.08s, 4.10s.

Both were consistent. If my understanding of the physics is correct then I will simply use them and then discuss how other factors may have impacted the results such as human error - (the filling of the syringes and manual timing). I'm definitely not going to manipulate my results to prove the physics. That defeats the purpose.
However if my understanding of the physics is incorrect, then I need to rectify that.

 

[Chestermiller]

What were the syringe barrel diameters? What was the liquid?

 

[LiamB]

I don't have the diameters recorded, just the difference in height to the 5mL fill line which was 8mm. The fluid is water.
I think I just had a lightbulb though. Can I use the equation of continuity in this situation even though it's not a closed system? If i do that, then my results make sense since an increase in cross-sectional area would mean a decrease in velocity, yes? So the 10mL syringe, with a larger cross-sectional area, would have fluid flow through it at a slower rate than the 5mL syringe.

 

[Chestermiller]

So the initial water level in the 5 cc syringe was 0.8 mm higher than in the 10 cc syringe. How do you feel that affected the initial flow rates?

 

[LiamB]

Well I was thinking initially that there would be a greater force on the outlet of the syringe but I'm not sure that's right because the total amount of fluid above the syringe outlet is the same in both cases.
I've read through my textbook but everything refers to fluid in/fluid out for fluid in motion and I'm dealing with an initially static fluid without adding anymore to the system.

 

[Chestermiller]

Well I was thinking initially that there would be a greater force on the outlet of the syringe but I'm not sure that's right because the total amount of fluid above the syringe outlet is the same in both cases.
I've read through my textbook but everything refers to fluid in/fluid out for fluid in motion and I'm dealing with an initially static fluid without adding anymore to the system.

Are familiar with hydrostatics or the Bernoulli equation?

 

[LiamB]

yes. but the (y) value will be always changing in this situation so i didn't think to use it here. hydrostatics tells us that pressure throughout a fluid is constant yes? and that any pressure applied to an enclosed system will be felt by the whole fluid uniformally. so the fluid at the bottom of the syringe is subject the the force of gravity, and the weight force of the fluid above it. which would suggest a higher initial flow rate in the smaller syringe. but would this not then diminish over time?

 

[Chestermiller]

yes. but the (y) value will be always changing in this situation so i didn't think to use it here. hydrostatics tells us that pressure throughout a fluid is constant yes?

No. The pressure is constant horizontally at each depth.
Toricelli's law (based on the bernoulli equation) tells us that the velocity at the exit hole is proportional to the square root of the height.

the weight force of the fluid above it. which would suggest a higher initial flow rate in the smaller syringe

That's better
.

but would this not then diminish over time?

The flow rate would diminish over time in both syringes.

Not only is the discharge velocity higher in the 5 ml syringe, but the cross sectional area of the barrel is less, so the height drops even faster still than in the 10 ml syringe.

 

[LiamB]

ok sweet. but would the larger syringe not then "catch up" if it is subject to a greater weight force once the smaller syringe discharges a certain amount? is it just a case of the first syringe gets a "head start"?

 

[Chestermiller]

ok sweet. but would the larger syringe not then "catch up" if it is subject to a greater weight force once the smaller syringe discharges a certain amount? is it just a case of the first syringe gets a "head start"?

You have all the information you need to quantify this, based on the Bernoulli equation. The parameters the come into play are the cross sectional area of the exit hole, the cross sectional area of the barrel, and the initial height. Do you think that, based on these parameters, you can derive an equation to estimate the discharge time?

 

[LiamB]

Hmm. Hadn't really thought to do that. I could definitely work out an equation for the velocity using the Bernoulli equation. especially if we used the outlet as h₀ or 0 (as a reference height) and the level of the fluid as h. But i still feel as though the velocity within the smaller diameter syringe would decrease much more rapidly as h decreases more rapidly and then wonder if the other syringe would catch up to it. That's the only thing now that I'm struggling to understand.

 

[Chestermiller]

Hmm. Hadn't really thought to do that. I could definitely work out an equation for the velocity using the Bernoulli equation. especially if we used the outlet as h₀ or 0 (as a reference height) and the level of the fluid as h. But i still feel as though the velocity within the smaller diameter syringe would decrease much more rapidly as h decreases more rapidly and then wonder if the other syringe would catch up to it. That's the only thing now that I'm struggling to understand.

Well, you can eliminate all the hand waving by just deriving the model. So why continue to speculate?

 

[LiamB]

I'm not sure how to work it out for time. but thanks for asking the right questions and making me think.

 

[Chestermiller]

Hmm. Hadn't really thought to do that. I could definitely work out an equation for the velocity using the Bernoulli equation. especially if we used the outlet as h₀ or 0 (as a reference height) and the level of the fluid as h. But i still feel as though the velocity within the smaller diameter syringe would decrease much more rapidly as h decreases more rapidly and then wonder if the other syringe would catch up to it. That's the only thing now that I'm struggling to understand.

Even if the height in the 5 ml syringe caught up with the height in the 10 ml syringe (and they were both discharging the same volume per unit time), the cross sectional area of the 5 ml syringe is smaller than the cross sectional area of the 10 ml syringe, so the height in the 5 ml syringe would still be falling faster.