Calculating Flow Rate in Syringe

[Rizer]

Hi all,

If I only know the Pressure given by a known Force on the barrel side of the syringe, the Density of the fluid, the Cross Section Area of the two parts of the syringe, the length of the syringe barrel and a ball with known Mass being pushed by the fluid flowing out of the syringe. How to know if the flow is steady or not? And how to calculate the gain in kinetic energy of the ball after the syringe is pushed to limit by the constant force?

Thx

 

[lightgrav]

If the Force applied to the barrel is constant, can you think of a reason that the flow wouldn't be?

If you do not know the viscosity of this fluid, you can't include its "friction",
so you can use Energy Conservation (even though it's unrealistic).
The original Pressure Potential Energy "PV" becomes KE of fluid and ball (plus the effect of grav.PE change, if there is any)

 

[Rizer]

Thank you, I just thought if the pressure is too large, the difference in pressure may lead to acceleration of fluid, there must be acceleration when the fluid start to flow. Can you teach me if there is any way to know how long or how far does it take to accelerate to constant flow?

And during constant flow, do I use Fs = KE or fluid in barrel and thin part + KE of ball? (is it ok to assume the ball reach constant speed as soon as the flow become constant?)

Or do I just need to apply Bernulli's eqn?
Using that, I have a problem on getting the pressure on the narrow side of syringe, as the reaction force given by the ball is keep changing as it is accelerating.

Thank you very much for answering me.

 

[lightgrav]

Bernoulli is usually useful ... .
Is this ball inside the syringe needle? If not, how can it provide a reaction Force?

I expect that the geometry is arranged so that (but where is this ball?)
Work done by the pusher (F dx = P dV) becomes KE of the ball, with the fluid stopping when it hits the ball (otherwise the integration could be outrageous, and you didn't mention a restitution coefficient).

But, to answer your question, you know the mass in the barrel (at v_b) and
the mass in the needle (at (A_b / A_n)*v_b ) .
The applied Force has to accelerate the ball (if it is inside the needle) and change some amount of barrel fluid (slow) into needle fluid (fast).
If the ball is inside the needle (or in the barrel), the resulting speed of the ball approaches the eventual speed exponentially, taking an infinite time to reach it exactly.

 

[Rizer]

Thx.
The ball is in the thinner part of syringe.

Can you explain why mass in the needle = (A_b / A_n)*v_b?

 

[Rizer]

And is it ok for me to use Bernulli's eqn, and add the KE expression of the ball on RHS?