Postural hypotension is the occurrence of low systolic blood pressure when a person stands up too quickly from a reclining position. A brain blood pressure lower than of can cause fainting or lightheadedness. In a healthy adult, the automatic constriction and expansion of blood vessels keep the brain blood pressure constant while posture is changing, but disease or aging can weaken this response. If the blood pressure in your brain is of while lying down, what would it be when you stand up if this automatic response failed? Assume your brain is from your heart and the density of blood is .
At this blood pressure will cause faintness.
The change in blood pressure as a person stands up can be modeled as the change in fluid pressure at different heights. Hence, it is fit to use the Bernoulli equation.
The mathematical form of Bernoulli's equation is as follows
Since the speed of the blood is considered as uniform, the above equation can be written as follows.
The variables in the above equation are described as follows.
: Blood pressure lying down, given as
: Blood pressure standing up, unknown
: Height lying down
: Height standing up
: Density of blood
: Acceleration due to gravity,
Isolate for from above equation.
Substitute for density of blood, for , for and for which is the distance between the heart and the brain, the same amount of displacement blood makes between heart and brain when person stands up
This blood pressure ,at , will cause nausea.
The two --diameter cylinders in FIGURE , closed at one end, open at the other, are joined to form a single cylinder, then the air inside is removed.
A. How much force does the atmosphere exert on the flat end of each cylinder?
B. Suppose one cylinder is bolted to a sturdy ceiling. How many football players would need to hang from the lower cylinder to pull the two cylinders apart?
It's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, , where is the height above sea level, is the density at sea level (you can use the Table value), and is called the scale height of the atmosphere.
a. Determine the value of .
Hint: What is the weight of a column of air?
b. What is the density of the air in Denver, at an elevation of ? What percent of sea-level density is this?
94% of StudySmarter users get better grades.Sign up for free