Final answer:
The concept in question is known as Orthostatic Hypotension and relates to the pressure changes when standing up quickly. Using the hydrostatic pressure equation and given values, the blood pressure at the head would be approximately 8.101 kPa if the body does not compensate for standing up from a lying position.
Step-by-step explanation:
When a person stands up quickly from a lying down position and experiences dizziness, this phenomenon is known as Orthostatic Hypotension, and it relates to changes in blood pressure. This question deals with calculating the changes in blood pressure assuming the person's body does not compensate for these changes.
To begin with, the gauge pressure at the heart is given to be 13.3 kPa. The question asks us to calculate the pressure at the head, which is 50.0 cm above the heart when the person stands up.
The pressure difference due to the height of a column of blood is given by the equation P = hρg, where P is the hydrostatic pressure increase, h is the height difference, ρ is the density of the blood, and g is the acceleration due to gravity.
Since gravity pulls blood downwards, standing up quickly results in a decrease in blood pressure at the head. For the purpose of an example calculation, let's consider the density of the blood to be 1,060 kg/m³, and the acceleration due to gravity as 9.81 m/s². Therefore, the pressure difference is 0.50 m * 1,060 kg/m³ * 9.81 m/s² = 5,199 Pa (or 5.199 kPa).
This pressure difference then needs to be subtracted from the pressure at the heart to find the pressure at the head. Doing the subtraction, we get 13.3 kPa - 5.199 kPa = 8.101 kPa. Hence, if the body doesn't compensate, the pressure at the head when the person stands up would be approximately 8.101 kPa.