A syringe which has an inner diameter of 0.6 mm is attached to a needle which has an inner diameter of 0.25 mm. A nurse uses the syringe to inject fluid into a patient's artery where blood pressure is 140/100. Assume the liquid is an ideal fluid. What is the minimum force the nurse needs to apply to the syringe?
f=0.005N
To find the minimum force the nurse needs to apply to the syringe, we need to consider the principles of fluid mechanics and the concept of pressure.
First, let's calculate the difference in pressure between the syringe and the artery. The pressure difference will determine the force required to push the fluid into the artery.
The blood pressure is given as 140/100. We need to convert this pressure to the SI unit of pressure, which is pascals (Pa). 1 mmHg is equal to 133.32 Pa.
Therefore, the arterial pressure is (140 mmHg) * (133.32 Pa / 1 mmHg) = 18,664.8 Pa.
The syringe pressure is (100 mmHg) * (133.32 Pa / 1 mmHg) = 13,332 Pa.
The pressure difference will be the arterial pressure minus the syringe pressure:
Pressure difference = 18,664.8 Pa - 13,332 Pa = 5,332.8 Pa.
Now, let's calculate the cross-sectional area of the syringe and the needle using their inner diameters.
Area of the syringe = π * (0.6 mm / 2)^2
Area of the needle = π * (0.25 mm / 2)^2
To convert the diameters from millimeters (mm) to meters (m), we divide by 1000:
Area of the syringe = π * (0.6 mm / 2 / 1000)^2
Area of the needle = π * (0.25 mm / 2 / 1000)^2
Next, calculate the force required to overcome the pressure difference by using the formula:
Force = Pressure difference * Area
Force = 5,332.8 Pa * (π * (0.6 mm / 2 / 1000)^2)
Force = 5,332.8 Pa * (π * (0.25 mm / 2 / 1000)^2)
Simplifying these equations will give you the minimum force required to apply.
It's important to note that this calculation assumes ideal fluid behavior and neglects factors like friction and viscosity. Additionally, other considerations such as the patient's condition, needle length, and user technique should also be taken into account to ensure safe and effective administration of medication.