Question

Find the pressure increase in the fluid in a syringe when a nurse applies a force of 42 Nto the syringe’s circular piston, which has a radius of 1.1 cm

Short answer

The pressure increase in the fluid is $1.1\times {10}^5\mathrm{Pa}$.

Step-by-step solution

The given data

1. The applied force is F=42 N
2. The radius of the piston is R = 1.1 cm

Understanding the concept of pressure

A fluid is a substance that can flow; it conforms to the boundaries of its container because it cannot withstand shearing stress. It can, however, exert a force perpendicular to its surface. If the force is uniform over a flat area, then the force is described in terms of pressurep.

We can use the formula for pressure$\left(p\right)$in terms of force applied$\left(F\right)$ to the given area$\left(A\right)$ to find the pressure increase in the fluid in the syringe.

$p=\frac{F}{A}$ …(i)

The area of the syringe’s circular piston can be found using the formula,

$A=\tau \tau R^2$ …(ii)

Calculation of the pressure increase in the fluid

Use the equation (i) to write the pressure increase in the fluid and substitute the given values,

$$\begin{gathered} R=1.1\mathrm{cm} \\ =0.011\mathrm{m} \\ p=\frac{F}{\tau \tau R^2} \\ =\frac{42\mathrm{N}}{\tau \tau {\left(0.011\mathrm{m}\right)}^2} \\ =1.1\times {10}^5\mathrm{Pa} \end{gathered}$$

Hence, the increased pressure in the fluid is $1.1\times {10}^5\mathrm{Pa}$.