Why do you feel dizzy if you stand up too quickly?
Blood travels from the heart through the major arteries down to the feet or up to the head. Ignoring branching of the arteries, we will consider the major arteries as columns of moving fluid. Bernoulli’s equation (Eqn.1) states that[note]Knight, R.D, Jones, B. and Field, S. College Physics: a strategic approach (1st ed.). Pearson Addison-Wesley, 2007.[/note]
$p_1 + \frac{1}{2} pv{_1}^2 + p g y_1 = p_2 + \frac{1}{2} pv{_2}^2 + p g y_2 \tag{1}$
where $p$ is the pressure of a fluid traveling velocity $v$ in a tube at vertical position $y$ and the subscripts $_1$ and $_2$ indicate different positions in the tube. Take one position where we want to know the pressure to be in a major artery just outside the heart and another to be in that artery where it extends to the feet. Assuming the velocity of the blood is roughly the same at both places then the difference in pressure from Bernoulli’s equation gives Eqn.2.
$p_\text{feet} – p_\text{heart} = p g (y_\text{heart} – y_\text{feet}) \tag{2}$
If you are lying down, then the vertical position of the heart and the feet is the same so that there is no pressure difference. If you are standing then the blood pressure in the feet is greater by $ฯg(y_\text{heart}-y_\text{feet})$. The heart is roughly 1.3 m above the feet and the density of blood is roughly that of water $\rho$ = 1000 kg/m3 so that the pressure in the artery at the foot is about 13 kPa greater than at the heart. Using the conversion of 1 atm = 101.3 kPa and 1 atm = 760 mmHg, that gives a difference of 96 mmHg. The average pressure in the major arteries at the heart is approximately 100 mmHg so that the pressure in the arteries at the feet for a standing individual would be 196 mmHg. Using a similar argument we can see that the pressure in major arteries will decrease leading to the head when standing.
The fact that blood pressure throughout the body varies depending on body position leads to physiological effects such as dizziness when standing up too quickly as a result of the sudden pressure drop causing a lack of blood flow to the brain. The increased blood pressure at the legs and feet when standing can cause increased fluid buildup in the legs which worsens conditions like edema (excessive fluid buildup) in the elderly and can cause people that have to stand still for extended periods of times (soldiers in a parade) to faint because of a lack of blood going to the brain[note]Tuszynski, Dixon, Biomedical Applications of Introductory Physics, 1st edition, p. 117-119, John Wiley & Sons, Inc.(2002)[/note].
Summary:
Blood pressure in major arteries will change with height difference relative to the heart which can lead to problems if body position is changed rapidly or certain positions are held for a long time.
Revised 2019-10-16
