= Solution
<Pascal's law> concerns a <pressure> increment imposed on a confined <fluid> at rest. A water-filled vessel with small openings in differently oriented walls and a close-fitting <piston> illustrates it: pressing the <piston> produces jets in different directions, showing that <pressure> acts normally to each local surface. Compare ports at the same height to remove differences of <hydrostatic pressure>. Pressure gauges at equally high ports show the same imposed increment after the disturbance settles.
For an ideal <hydraulic press> with <piston> areas $A_1,A_2$,
$$
\boxed{\Delta p=\frac{F_1}{A_1}=\frac{F_2}{A_2},\qquad F_2=F_1A_2/A_1.}
$$
Conservation of <fluid> volume gives $A_1s_1=A_2s_2$, hence $F_1s_1=F_2s_2$: the larger output <force> accompanies a smaller <displacement> and does not create <energy>.
\b[The arterial pulse is not simultaneous throughout the body.] <Pascal's law> is an equilibrium statement, not instantaneous transmission. An <arterial pulse> travels through coupled <blood> and elastic arterial walls. Synchronized recordings at two sites show different arrival times of corresponding waveform features. For effective propagation distance $L$, <pulse wave velocity> is $c_p=L/\Delta t$. It differs from the transport <velocity> of individual blood cells.<2024 Recommendations for Validation of Noninvasive Arterial Pulse Wave Velocity Measurement Devices>[Transit-time estimation from pressure waveforms; diastolic-foot detection and temporal resolution]{ref}
A bench demonstration uses an elastic liquid-filled tube, two pressure sensors at known positions, and a short pressure pulse at one end. The delayed second recording tests finite <pressure wave propagation> independently of the eventual static <pressure> balance.
\Image[/past-exam-of-the-medicine-course-of-the-university-of-oxford/1867/first-examination/physics-1867-pulse-transit.png]
{title=An illustrative pressure pulse reaches the second sensor later; these curves are a model rather than patient data}
Back to article page
