# Calculate the pressure?

1. Sep 26, 2016

### Derek1997

1. The problem statement, all variables and given/known data
Jane, a vet, is trying to sedate a dog by injecting him with sedative in a hypodermic syringe that
has a needle 20mm long with internal diameter 0.4 mm. The vet wishes to inject the dog with
3 ml of anaesthetic that has viscosity 4 x10^-3 Pas. Since the dog is struggling hard, she needs
to get it into his bloodstream within 1 second.
(a) How much pressure needs to be applied to the fluid in the syringe barrel to achieve this
rate of flow through the needle?
(b) Explain why this is pressure is not absolute, but is relative to atmospheric pressure.
(c) If the barrel of the syringe is 10mm in diameter, what force does Jane need to apply to the
plunger to achieve the needed flow rate

2. Relevant equations
Poiseullie or Bernouli

3. The attempt at a solution
Hi there, I'm stuck at this question. I don't know if I should use pensoulli's equation or bernoulis! Well the question did ask how much pressure, but idk how to tackle this question :( I'm seeking advise please

2. Sep 26, 2016

### Bystander

Are you looking for flow rate? Or, energy conservation? Which equation applies?

3. Sep 26, 2016

### Derek1997

Flow rate I think. But again it asked for pressure also so i don't know where to start with.

4. Sep 26, 2016

### Bystander

Which equation depends on ΔP?

5. Sep 26, 2016

### Derek1997

heres what I think, so Q is flow rate right? can we do 3ml/1= 3ml/s? then sub the value inside the it into the poiseulles equation?

6. Sep 26, 2016

### Bystander

Yup.

7. Sep 26, 2016

### Derek1997

is it actually?

8. Sep 26, 2016

### Bystander

It is; you'll have to convert/invert between CGS & MKS units (ml, Pa⋅s, mm, and so on).

9. Sep 26, 2016

### Derek1997

alright, so heres what I've done=
delta p= 8*u*L.Q/pi*r^4
where I got my Q as 3m/s
I converted my Length into 0.02m
R= 0.0004m
Then i subbed the value inside equation as = 8.4x10^-3pa x 0.02m x 3m/s / pi x 0.0004^4= 2.38x10^10pa which looks weird!

10. Sep 26, 2016

### Bystander

That looks high to me; can you double check it?

11. Sep 26, 2016

### Derek1997

I did but still yeilds me the same, although I'm not sure about one thing.. for r i used "internal diamater 0.4mm" which i converted to meters?

12. Sep 26, 2016

### Bystander

Not 8.4 ...
One milliliter is 10-6 m3.

13. Sep 26, 2016

### Derek1997

haha I didn't do 8.4 it was type mistake, also in regard to radius, we are not given how am I suppose to find it?

14. Sep 26, 2016

### Bystander

Half the diameter?

15. Sep 26, 2016

### Derek1997

Thanks mate, I gave you a life :) p.s if u had time check out my other question as well. Thanks

16. Sep 26, 2016

### Derek1997

like* haha

17. Sep 26, 2016

### Bystander

All nighter?

18. Sep 26, 2016

### Derek1997

Nein, im finished with my chem so im about to sleep haha