Question

You inflate the front tires on your car to$\mathbf{28}\mathbf{}\mathit{p}\mathit{s}\mathit{i}$. Later, you measure your blood pressure, obtaining a reading of 120/80 , the readings being in $\mathit{m}\mathit{m}\mathbf{}\mathit{H}\mathit{g}$. In metric countries (which is to say, most of the world), these pressures are customarily reported in kilopascals$\left(kPa\right)$. In kilopascals, (a) what is your tire pressure? And (b) what is your blood pressure?

Short answer

a) The tire pressure is $192.4kPa$.

b) The blood pressure is $15.9kPa$or $10.6kPa$.

Step-by-step solution

The given data

1. Pressure of tire,$p_t=28psi\mathrm{or}28lb/i{n}^2$

1. High and low blood pressure,$p_b=120mmHg$and$80mmHg$

Understanding the concept of pressure

We can use the dimensional analysis concept to find the pressure in tire and blood in kPa. Using conversion factors between psi$\mathit{l}\mathit{b}\mathbf{/}\mathit{i}{\mathit{n}}^{\mathbf{2}}$ and$\mathit{l}\mathit{b}\mathbf{/}\mathit{i}{\mathit{n}}^{\mathbf{2}}$ between Pa and , we can findthepressure in the tire in kPa. Then using the conversion factor between mm Hg and Pa, we can find the blood pressure in kPa.

Formula:

Pressure on a body by force F on an area A,

$p=\frac{F}{A}$ (i)

a) Calculation for tire pressure in kPa

$$\begin{gathered} p_t=28lb/i{n}^2\times \frac{1.01\times {10}^{5}Pa}{14.7lb/i{n}^2}\left(\because 1atm=1.01\times {10}^{5}Pa=lb/i{n}^2\right) \\ =192.4kPa \end{gathered}$$ Hence, the tire pressure value is 192.4 kPa.

b) Calculation for blood pressure in kPa

Calculation for 120 mmHg:

$$\begin{gathered} p_b=120mmHg\times \frac{1.01\times {10}^{5}Pa}{760mmHg}\left(\because 1atm=1.01\times {10}^{5}Pa=lb/i{n}^2\right) \\ =15.9kPa \end{gathered}$$Calculation for 80 mmHg:

$$\begin{gathered} p_b=80mmHg\times \frac{1.01\times {10}^{5}Pa}{760mmHg}\left(\because 1atm=1.01\times {10}^{5}Pa=lb/i{n}^2\right) \\ =10.6kPa \end{gathered}$$ Hence, the blood pressure values are 15.9 kPa and 10.6 kPa for 120mmHg and 80mmHg respectively.