When you suddenly stand up after lying down for a while, your body may not compensate quickly enough for the pressure changes and you might feel dizzy for a moment.
(a) If the gauge pressure of the blood at your heart is 15.02 kPa and your body doesn't compensate, what would the pressure be at your head, 49.6 cm above your heart?
Answer in kPa
(b) If the gauge pressure of the blood at your heart is 15.02 kPa and your body doesn't compensate, what would it be at your feet, 1.30 ✕ 10^2 cm below your heart? Hint: The density of blood is 1060 kg/m3.
Answer in kPa
well, I used 1000 for rho before I saw the hint so you use 1060
rho g h=1000*9.81*.496 = 4.86* 10^3 Pa
which is 4.86 k Pa
15.02 - 4.86 = 10.15 k Pa
rho g h = 1000*9.81*1.3 = 12.75 k Pa
15.02 + 12.75 = 27.8 k Pa
To answer these questions, we can use the concept of hydrostatic pressure. The hydrostatic pressure at a certain point in a fluid is given by the formula:
P = P0 + ρgh
Where:
P is the pressure at the given point,
P0 is the pressure at the reference point (usually the heart),
ρ is the density of the fluid (in this case, blood),
g is the acceleration due to gravity, and
h is the height difference between the given point and the reference point.
(a) For the pressure at your head, 49.6 cm above your heart, we have:
P0 = 15.02 kPa,
h = 49.6 cm = 0.496 m,
ρ = 1060 kg/m³,
g ≈ 9.8 m/s².
Plugging these values into the formula, we get:
P = 15.02 kPa + (1060 kg/m³)(9.8 m/s²)(0.496 m)
Calculating this expression will give the pressure at your head.
(b) For the pressure at your feet, 1.30 ✕ 10^2 cm below your heart, we have:
P0 = 15.02 kPa,
h = -1.30 ✕ 10^2 cm = -1.30 m,
ρ = 1060 kg/m³,
g ≈ 9.8 m/s².
Notice that in this case, h is negative because the feet are below the heart. Plugging these values into the formula, we get:
P = 15.02 kPa + (1060 kg/m³)(9.8 m/s²)(-1.30 m)
Again, calculating this expression will give the pressure at your feet.
To answer these questions, we can use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at a given point that is due to the weight of the fluid column above that point.
(a) To find the pressure at your head, 49.6 cm above your heart, we can use the equation for hydrostatic pressure:
P = P₀ + ρgh
where:
P is the pressure at the desired location,
P₀ is the pressure at the reference location (heart),
ρ is the density of the fluid (blood),
g is the acceleration due to gravity,
and h is the height difference between the desired location and the reference location.
Given:
P₀ = 15.02 kPa,
h = 49.6 cm = 0.496 m.
The density of blood, ρ, is 1060 kg/m³.
We can now calculate the pressure at the head:
P = 15.02 kPa + (1060 kg/m³) * (9.8 m/s²) * (0.496 m)
P ≈ 15.02 kPa + 5170.88 Pa
P ≈ 15.02 kPa + 5.17 kPa
P ≈ 20.19 kPa
Therefore, the pressure at your head, 49.6 cm above your heart, would be approximately 20.19 kPa.
(b) To find the pressure at your feet, 1.30 × 10² cm below your heart, we can use the same equation for hydrostatic pressure.
Given:
P₀ = 15.02 kPa,
h = -1.30 × 10² cm = -1.30 m (negative because it is below the heart).
We can now calculate the pressure at the feet:
P = 15.02 kPa + (1060 kg/m³) * (9.8 m/s²) * (-1.30 m)
P ≈ 15.02 kPa - 15039.2 Pa
P ≈ 15.02 kPa - 15.04 kPa
P ≈ -0.02 kPa
Therefore, the pressure at your feet, 1.30 × 10² cm below your heart, would be approximately -0.02 kPa.
Please note that negative pressure values may not have a physical meaning in this context.