Question

Explain why
A. The blood pressure in humans is greater at the feet than at the brain
B. Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km.
C. Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

Answer 1

Hint: All three sub-parts are related to pressure. The relation between pressure and height can be used for the first sub-part. Using the relation between height, density and pressure, the second sub-part can be answered. The third sub-part is based on Pascal's law.

Formula used:
$P\quad =\quad \rho gh$

Complete step by step answer:
A. Blood pressure is defined as the force exerted by the column of blood on the artery walls. We know, the relation between height and pressure is given by,
$P\quad =\quad \rho gh$ …(1)
where, $\rho$: density
              h: height
              g: acceleration due to gravity
From the above equation, it can be inferred that height is directly proportional to pressure. Thus, blood pressure depends on the height. At the feet, the height of the blood column is more as compared to that at the brain. Hence, blood pressure in humans is greater at the feet than at the brain.

B. The density of air is the maximum near sea-level. From the equation. (1) it can be inferred height is inversely proportional to density of air. Thus, as height from the surface increases, the density of air decreases. At a height of about 6km, density decreases to nearly half of its value at sea level. And we know, atmospheric pressure is directly proportional to density. Hence, atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100km.

C. A scalar quantity is a quantity that has only magnitude. While vector quantity is a quantity that has both magnitude and direction.
According to Pascal’s Law, when force is applied to a fluid, the pressure in the fluid gets transmitted in all the directions. Thus, hydrostatic pressure does not have a fixed direction. Hence, it is a scalar quantity.

Note:
Hydrostatic Pressure and Atmospheric Pressure are similar but not the same. Hydrostatic Pressure is the pressure exerted by an incompressible liquid. While atmospheric pressure is a pressure exerted by a compressible fluid.