Question

Explain why the size of needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor where administrative an injection.

Answer 1

it is based on the concept given by Bernoulli.
according to Bernoulli's theorem, we know that
$P+\rho gh+\frac{1}{2}\rho v^2=\textbf{constant}$

according to equation of continuity, $\textbf{area}\times\textbf{velocity}=\textbf{constant}$,
if diameter of the needle is very less.so, flow velocity through the needle will be very high.

So needle controls the velocity of the fluid flow
By using our thumb we apply more pressure to the flow of fluid . So thumb controls pressure.
see Bernoulli's equation , The power of pressure is 1 and the power of velocity is 2. Thus size of the needle has more control over the flow rate than the thumb pressure.