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Q9.1: NCERT Physics - Part 2 MECHANICAL PROPERTIES OF FLUIDS 9.1 Solution: Explain why (a) The blood pressure in humans is greater at the…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently apply the simple hydrostatic formula $p=\rho g h$ with a constant density to the entire atmosphere (or to blood) and expect a linear pressure drop with height; in reality air density falls with altitude, giving an exponential pressure decrease, so pressure is about half at ~6 km even though the atmosphere extends >100 km. Remember to account for the variation of $ ho$ (or use the barometric equation) when dealing with large vertical extents.
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.
Step-by-Step Verified Solution
**Answer:** (a) Due to height difference. (b) Density of air decreases with height. (c) Force is a vector, but pressure is the normal component of force per unit area, which has no direction.
**Step-by-Step Explanation:**
(a) The blood pressure at a point depends on the height of the blood column above it. The column above the feet is much taller than the column above the brain. Hence, blood pressure at the feet is greater [citation:1].
(b) Atmospheric pressure decreases with height because the density of air decreases with altitude. At about 6 km, the density is roughly half its value at sea level, so the pressure is also about half. The atmosphere extends beyond 100 km, but the air there is extremely thin and contributes negligibly to pressure [citation:1].
(c) Pressure is defined as the magnitude of the normal force acting per unit area. Since the direction of the force is always perpendicular to the surface, and only its magnitude is used, pressure is a scalar quantity [citation:1].
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