I have been given this question and with very little knowledge of physics and a book and flex studies that I am not finding very explanitory. I am not sure I am on the correct path as the vlaues I have seem very large. I would appreciate any help/assistance anyone could give.
Question
You measure the blood pressure at the bicep and find that it is 140 mmHg systolic and 80mmHg diastolic. What would you expect the blood pressure to be at the top of the head given that this point is 45cm above the measurement point? Remember thisis a gauge pressure and give your answers in both mmHg and kPa. (The density of blood is about 1060 kgm^-3)
This is what I have done but I am so unsure on what I am doing.
1. Converted the systolic and diastolic blood pressure into Pa.
Systolic Blood pressure= 140mmHg x 133.322Pa/1mmHg= 18665 Pa
Diastolic Blood pressure= 80mmHg x 133.322Pa/1mmHg= 10665.76Pa
2. Due to being gauge pressure I then converted to actual pressure. (this is something I am very unsure if it is needed)
P1 actual systolic pressure= 18665Pa + 101325Pa = 119990Pa
P1 actual diastolic pressure= 10665.76Pa + 101325Pa = 111990.76Pa
3. Due to the change in hieght I named the top of the head P2.
P2 - P1=pg h2-h1
P2=P1+pgh
P2 systolic = 119990Pa + (1060kgm^-3 x 9.81 m s^-2 x 45m) = 587927Pa
P2 diastolic = 111990.76 + ( 1060kgm^-3 x 9.81 m s^-2 x 45m) = 579928Pa
4. I then converted the P2 into kPa.
P2 systolic kPa = 587927Pa x .1kPa/100Pa = 587.9kPa
P2 diastolic KPa = 579928Pa x .1kPa/100Pa = 579.9kPa
5. I then converted the P2 into mmHg. (this seems very large)
P2 systolic mmHg = 587927Pa x 1mmHg/133.322Pa = 4410mmHg
P2 diastolic mmHg = 579928Pa x 1mmHg/133.322Pa=4350mmHg
I have spent a lot of time trying to work this out. If you can please assist me I would be very greatful
Both pressures will be higher by pressure = (rho)*g*H when measured at elevation H higher than the arm. rho is the density of blood. Assume it is the same as water
Your numbers are much too high.
Atmospheric pressure is 760 mm Hg
450 mm higher elevation is equivalent to 45/13.6 = 33 mm Hg higher pressure, measured in mm Hg. The 13.6 factor id the ratio of the densities of mercury and water.
Pressures in the head will be lower, not higher, because of the higher elevation than the measurement point.
The number is also wrong:
It should be 45 mmHg/13.6 = 3.3 mmHg lower
I just wasn't thinking and apologize for the errors.
Thank you for your help. I am still unsure on the formulas I am meant to be using and when I am meant to be converting from mmHg to Pa.
It seems like you have made some errors in your calculations, particularly during the conversion steps. Let me go through the problem with you step by step, and explain how to correctly solve it.
Given data:
- Blood pressure at the bicep: 140 mmHg systolic and 80 mmHg diastolic
- Height difference from the bicep to the top of the head: 45 cm
- Density of blood: 1060 kg/m³
Step 1: Convert the blood pressures from mmHg to Pa.
1 mmHg = 133.322 Pa
Systolic blood pressure:
140 mmHg x 133.322 Pa/mmHg = 18,664.88 Pa
Diastolic blood pressure:
80 mmHg x 133.322 Pa/mmHg = 10,665.76 Pa
Step 2: Calculate the gauge pressure at the top of the head.
Since the problem specifies that the blood pressure values are gauge pressures, we need to add the atmospheric pressure to the given pressures.
Standard atmospheric pressure = 101,325 Pa
Gauge pressure at the top of the head (systolic):
18,664.88 Pa + 101,325 Pa = 120,989.88 Pa
Gauge pressure at the top of the head (diastolic):
10,665.76 Pa + 101,325 Pa = 112,990.76 Pa
Step 3: Convert the gauge pressure to absolute pressure.
This step is not required because we need to determine the gauge pressure at the top of the head as well. So now we have the absolute pressure values directly.
Step 4: Apply the hydrostatic pressure equation.
The equation for hydrostatic pressure is P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height difference.
Gauge pressure at the top of the head (systolic):
P2 = 120,989.88 Pa + (1060 kg/m³ x 9.81 m/s² x 0.45 m) = 125,764.19 Pa
Gauge pressure at the top of the head (diastolic):
P2 = 112,990.76 Pa + (1060 kg/m³ x 9.81 m/s² x 0.45 m) = 117,564.87 Pa
Step 5: Convert the pressures to the desired units.
To convert the pressures to mmHg, use the conversion factor: 1 mmHg = 133.322 Pa.
Gauge pressure at the top of the head (systolic):
125,764.19 Pa x 1 mmHg/133.322 Pa = 943.26 mmHg
Gauge pressure at the top of the head (diastolic):
117,564.87 Pa x 1 mmHg/133.322 Pa = 881.88 mmHg
Step 6: Convert the pressures to kPa.
To convert the pressures to kPa, use the conversion factor: 1 kPa = 1000 Pa.
Gauge pressure at the top of the head (systolic):
125,764.19 Pa x 0.001 kPa/1 Pa = 125.76 kPa
Gauge pressure at the top of the head (diastolic):
117,564.87 Pa x 0.001 kPa/1 Pa = 117.56 kPa
Therefore, the blood pressure at the top of the head (gauge pressure) would be approximately 943.26 mmHg systolic and 881.88 mmHg diastolic, or 125.76 kPa systolic and 117.56 kPa diastolic.