91影视

The expression for the force is,

$F=PA$

Here, $P$ is the pressure and A is the area.

(A)The area of the syringe is,

$A={\mathrm{蟺谤}}^2$

Here, $r$is the radius of the syringe

Substitute $\frac{d}{2}$for $r$.

$A=蟺{\left(\frac{d}{2}\right)}^2$

Here, $d$is the diameter.

Substitute $6mm$for $d$.

$A=蟺{\left(\frac{6\mathrm{mm}\left(\frac{1\mathrm{m}}{1000\mathrm{mm}}\right)}{2}\right)}^2$

$=2.83脳{10}^{-5}{\mathrm{m}}^2$

$P=\left(100\mathrm{mmHg}\right)\left(\frac{1\mathrm{atm}}{760\mathrm{mmHg}}\right)\left(\frac{1.013脳{10}^5\mathrm{Pa}}{1\mathrm{atm}}\right)$

$=13.32脳{10}^3\mathrm{Pa}$

So, the minimum force is,

$F=PA$

Substitute $2.83脳{10}^{-5}{\mathrm{m}}^2$for $A$and $13.32脳{10}^3\mathrm{Pa}$for $P$.

$F=\left(13.32脳{10}^3\mathrm{Pa}\right)\left(2.83脳{10}^{-5}{\mathrm{m}}^2\right)$

$=0.38N$

Hence, the required force is $0.38N$

(B)The volume flow rate is,

$Q=\frac{V}{t}$

Here, $V$is the volume and $t$is the time.

Substitute $2mL$for $2s$and for $t$.

$Q=\frac{2\mathrm{mL}\left(\frac{{10}^{-6}{\mathrm{m}}^3}{1\mathrm{mL}}\right)}{2\mathrm{s}}$

$=1脳{10}^{-6}{\mathrm{m}}^3/\mathrm{s}$

The area of the needle is,

Substitute $\frac{d}{2}$for r

$A=蟺{\left(\frac{d}{2}\right)}^2$

Substitute $0.125mm$for $d$

$A=蟺{\left(\frac{0.125\mathrm{mm}\left(\frac{1\mathrm{m}}{1000\mathrm{mm}}\right)}{2}\right)}^2$

$=4.91脳{10}^{-8}{\mathrm{m}}^2$

The flow rate is,

$Q=Av$

$v=\frac{Q}{A}$

Substitute $4.91脳{10}^{-8}{\mathrm{m}}^2$for $A$and$1脳{10}^{-6}{\mathrm{m}}^3/\mathrm{s}$for $Q$.

$v=\frac{1脳10{\mathrm{m}}^3/\mathrm{s}}{4.91脳{10}^{-8}{\mathrm{m}}^2}$

$=20.4\mathrm{m}/\mathrm{s}$

As a result, the necessary speed is $20.4m/s$.