In this problem, we examine the hydrostatic pressure in a fluid at rest.(a) Consider a small fluid element $Δ x \times Δ y \times Δ z$ at rest. Write down the balance of forces on the fluid element due to the fluid pressure $p$ and the gravitational pull of the Earth. Show that this leads to the differential equation $\nabla p = ρ g$ where $g$ is the acceleration due to gravity.(b) Solve the differential equation derived in (a) assuming a uniform fluid density. Show that the pressure in the fluid is given by $p (z) = p_{0} - ρ g z,$ where the z-axis is in the direction opposite to g.(c) Estimate the atmospheric pressure. (Hint: Look up the density of air and make a reasonable guess for the height of the atmosphere.)(d) If you raise your arm above your head as the doctor is measuring your blood pressure, how much will the measurement change compared with when you keep your arm level with the heart. Try it next time you are at the doctor's officel

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In this problem, we examine the hydrostatic pressure in a fluid at rest.(a) Consider a small fluid element

Δ x \times Δ y \times Δ z

at rest. Write down the balance of forces on the fluid element due to the fluid pressure

p

and the gravitational pull of the Earth. Show that this leads to the differential equation

\nabla p = ρ g

where

g

is the acceleration due to gravity.(b) Solve the differential equation derived in (a) assuming a uniform fluid density. Show that the pressure in the fluid is given by

p (z) = p_{0} - ρ g z,

where the z-axis is in the direction opposite to g.(c) Estimate the atmospheric pressure. (Hint: Look up the density of air and make a reasonable guess for the height of the atmosphere.)(d) If you raise your arm above your head as the doctor is measuring your blood pressure, how much will the measurement change compared with when you keep your arm level with the heart. Try it next time you are at the doctor's officel

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Question Text	In this problem, we examine the hydrostatic pressure in a fluid at rest.(a) Consider a small fluid element $Δ x \times Δ y \times Δ z$ at rest. Write down the balance of forces on the fluid element due to the fluid pressure $p$ and the gravitational pull of the Earth. Show that this leads to the differential equation $\nabla p = ρ g$ where $g$ is the acceleration due to gravity.(b) Solve the differential equation derived in (a) assuming a uniform fluid density. Show that the pressure in the fluid is given by $p (z) = p_{0} - ρ g z,$ where the z-axis is in the direction opposite to g.(c) Estimate the atmospheric pressure. (Hint: Look up the density of air and make a reasonable guess for the height of the atmosphere.)(d) If you raise your arm above your head as the doctor is measuring your blood pressure, how much will the measurement change compared with when you keep your arm level with the heart. Try it next time you are at the doctor's officel
Topic	All topics
Subject	Biology
Class	Class 11

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