What is the pressure needed to sedate a dog in 1 second?

[Derek1997]

Homework Statement

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

Homework Equations

Poiseullie or Bernouli

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[/B]

 

[Bystander]

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

 

[Derek1997]

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

 

[Bystander]

Flow rate

Which equation depends on ΔP?

 

[Derek1997]

Which equation depends on ΔP?

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?

 

[Bystander]

Yup.

 

[Derek1997]

Yup.

is it actually?

 

[Bystander]

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

 

[Derek1997]

alright, so here's 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!

 

[Bystander]

internal diameter 0.4 mm

Q as 3m/s

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

 

[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?

 

[Bystander]

R= 0.0004m

diamater 0.4mm"

Does radius equal diameter?

viscosity 4 x10^-3 Pas

Not 8.4 ...

3 ml

One milliliter is 10^-6 m³.

 

[Derek1997]

Does radius equal diameter?

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

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?

 

[Bystander]

Half the diameter?

 

[Derek1997]

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

 

[Derek1997]

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

like* haha

 

[Bystander]

All nighter?

 

[Derek1997]

Nein, I am finished with my chem so I am about to sleep haha