Calculate the pressure in newtons per square meter due to whole
blood in an IV system, such as the one shown in Figure 6.9, if h = 1.5 m. (b)
Noting that there is an open tube, so that atmospheric pressure is exerted on the
blood in the bottle, calculate the total pressure exerted at the needle by the blood.
Ah, the pressure game with some IV humor! Well, let's get to it.
To calculate the pressure in newtons per square meter (also known as pascals), we'll need two things: the height of the blood column and the density of the blood.
Now, assuming you're not pulling my leg with a blood-filled IV system, we have h = 1.5 m. As for the density of whole blood, it's around 1,060 kilograms per cubic meter.
To find the pressure, we use the formula:
Pressure = height x density x gravity
So, Pressure = 1.5 m x 1,060 kg/m³ x 9.8 m/s²
Just crunch the numbers, and you'll know the pressure in pascals. But remember, I'm just a humble humor bot, and this is not certified medical advice. So, if you're really in a pinch, please consult a qualified professional. They'll ensure your humor levels are balanced too!
To calculate the pressure exerted by the blood in an IV system, we need to consider the pressure due to the height of the blood column and the atmospheric pressure.
Step 1: Calculate the pressure due to the height of the blood column.
The pressure due to the height of the blood column can be calculated using the equation:
Pressure = density * gravitational acceleration * height
Given:
density of blood (ρ) = 1,060 kg/m³ (approximately)
gravitational acceleration (g) = 9.8 m/s² (approximately)
height (h) = 1.5 m
Using these values in the equation, we can calculate the pressure due to the height of the blood column.
Pressure = ρ * g * h
Pressure = 1,060 kg/m³ * 9.8 m/s² * 1.5 m
Step 2: Calculate the atmospheric pressure.
The atmospheric pressure is typically around 101,325 pascals (Pa).
Step 3: Calculate the total pressure exerted at the needle by the blood.
Since the tube is open, atmospheric pressure is exerted on the blood in the bottle. Therefore, the total pressure at the needle will be the sum of the pressure due to the blood column and the atmospheric pressure.
Total Pressure = Pressure due to the height of the blood column + Atmospheric Pressure
Now you can substitute the values into the equation and calculate the total pressure exerted at the needle by the blood.
To calculate the pressure exerted by the blood in an IV system, we need to take into account the height of the liquid column and the atmospheric pressure.
The pressure exerted by a liquid is given by the equation:
P = ρgh
Where:
P is the pressure
ρ is the density of the liquid
g is the acceleration due to gravity
h is the height of the liquid column
In this case, we are dealing with blood, which has a density of about 1,060 kg/m^3.
So, to calculate the pressure due to the blood in the IV system:
Step 1: Convert the height of the liquid column from meters to centimeters.
Since 1 meter is equal to 100 centimeters, we have:
h = 1.5 m * 100 cm/m = 150 cm
Step 2: Convert the density of blood from kg/m^3 to g/cm^3.
Since 1 kg is equal to 1,000 grams and 1 m^3 is equal to 1,000,000 cm^3, we have:
ρ = 1,060 kg/m^3 * 1 g/1000 kg * 1 m^3/1,000,000 cm^3 = 1.06 g/cm^3
Step 3: Calculate the pressure exerted by the blood.
Using the equation P = ρgh, we have:
P = 1.06 g/cm^3 * 9.8 m/s^2 * 150 cm = 1,569 g·cm/s^2
To convert this to Newtons per square meter (Pa), we need to divide by 100 (since 1 N = 100 g·cm/s^2):
P = 1,569 g·cm/s^2 / 100 = 15.69 N/m^2
So, the pressure exerted by the blood in the IV system, at the needle, is approximately 15.69 N/m^2 (or 15.69 Pa).
Note: In this calculation, we neglected any additional pressure from the flow rate and resistance of the IV system, and assume that the needle is at the same height as the liquid column.