The patient in the figure below is to receive an intravenous injection of medication. In order to work properly, the pressure of fluid containing the medication must be 108 kPa at the injection point.
(a) If the fluid has a density of 1024 kg/m3, find the height at which the bag of fluid must be suspended above the patient. Assume that the pressure inside the bag is one atmosphere.
Your response differs from the correct answer by more than 10%. Double check your calculations. m
(b) If a less dense fluid is used instead, must the height of suspension be increased or decreased?
1 atm =101300 Paá
p=p₀+ρgh= =>
h=(p-p₀)/ρg =
=(108000 -101300)/ 9.8•1024=
=0.668 m
If ρ₂<ρ₁, h₂>h₁
b)
The formula for calculation height is
h=P1-P / pg
where P1 is the pressure of the fluid. P is atmospheric pressure. p is the density of fluid. g is the gravitational accelertion (9.81 ms^-2)
clearly, there is an inverse relationship between height and density. i.e. if height increases, density of fluid used must be lower, and if height decreases, the density of the fluid must be higher. The question asks whether the height of suspension should increase or decrease if a less dense fluid is used, and the answer to that is height must definitely increase.
Yes of course should increase but why so
(a) Well, it seems like we have a patient who needs some medication. Let's find out how high we have to hang that bag of fluid. To do this, we can use the good old hydrostatic pressure equation: P = ρgh. Here, P is the desired pressure of 108 kPa, ρ is the density of the fluid at 1024 kg/m^3, g is the acceleration due to gravity at 9.8 m/s^2, and h is the height we're looking for.
Plugging in the numbers, we have 108,000 Pa = (1024 kg/m^3)(9.8 m/s^2)(h). Now let's do some math. Dividing both sides by (1024 kg/m^3)(9.8 m/s^2), we find h ≈ 10.9 meters. So, the bag of fluid needs to be suspended about 10.9 meters above the patient.
But hey, my calculations may not be perfect, so double-check them just to be sure!
(b) If a less dense fluid is used, like helium or air, then we would need to increase the height of suspension. You see, the pressure at the injection point depends on the density of the fluid and its height. If we use a less dense fluid, we'll need to compensate by increasing the height to achieve the desired pressure. It's like trying to balance things out. So, in short, if the fluid is less dense, we'll have to go higher to keep things in check.
To find the height at which the bag of fluid must be suspended above the patient, we can use the concept of pressure and the equation for pressure in a fluid.
(a) The pressure at a given point in a fluid is given by the equation:
P = ρgh,
where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
In this case, we know that the pressure at the injection point should be 108 kPa, which is equivalent to 108,000 Pa. We also know that the density of the fluid is 1024 kg/m3, and the pressure inside the bag is one atmosphere, which is equivalent to 101,325 Pa.
First, let's convert the pressure to the same units:
108 kPa = 108,000 Pa.
Now, we can rearrange the equation to solve for h:
h = P / (ρg).
Substituting the values:
h = 108,000 Pa / (1024 kg/m3 × 9.8 m/s2).
Calculating the result gives:
h ≈ 10.7 meters.
Therefore, the height at which the bag of fluid must be suspended above the patient is approximately 10.7 meters.
Please note that the correct answer may differ from this calculated value by more than 10%. Double-check your calculations to ensure accuracy.
(b) If a less dense fluid is used, the height of suspension must be increased. This is because the pressure at the injection point is determined by the height of the fluid column. With a less dense fluid, the same pressure would require a greater height to generate the necessary pressure at the injection point.