Solving Pressure of Syringe Homework Statement

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SUMMARY

The discussion focuses on calculating the minimum force required to inject medicine using a 2.0 mL syringe with specific dimensions and the flow speed of the medicine through a 0.25 mm needle. The minimum pressure needed for injection was calculated as 18659.2 Pa, leading to a required force of 0.377 N when applying the formula P = F/A using the syringe's inner diameter of 6.0 mm. Additionally, the flow speed of the medicine was determined to be 20.4 m/s, calculated using the area of the needle and the principle of continuity (Av = constant).

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Knowledge of pressure calculations using P = F/A.
  • Familiarity with area calculations for circular cross-sections.
  • Basic grasp of unit conversions, particularly between mm Hg and Pascals.
NEXT STEPS
  • Study Bernoulli's equation and its applications in fluid mechanics.
  • Learn about pressure conversions, specifically from mm Hg to Pascals.
  • Explore the concept of flow rate and its relationship to cross-sectional area in fluid systems.
  • Investigate syringe mechanics and how different diameters affect force and flow rates.
USEFUL FOR

Students in physics or engineering courses, healthcare professionals using syringes for injections, and anyone interested in fluid dynamics and pressure calculations.

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Homework Statement


A 2.0 mL syringe has an inner diameter of 6.0mm, a needle inner diameter of 0.25mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100.
a. What is the minimum force the nurse needs to apply to the syringe?
b. The nurse empties the syringe in 2.0s. What is the flow speed of the medicine through the needle?

Homework Equations


P = pgh
0.5pv^2 + pgh + P = constant
Av = constant
P = F/A

The Attempt at a Solution


Using P = pgh, I found the minimum pressure required to inject the medicine to be 18659.2 Pa. I tried to plug that into P=F/A but didn't get the right answer. For a, the answer is supposed to be 0.377N and for b, 20.4m/s. Does anyone know how to get these answers? Thanks.
 
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convert 100mm Hg into Pa...

Then use that in P = F/A, where A is the area of the inner diameter, 6.0mm.

Then use the 0.25mm area to get the flow velocity.
 
how do you get the flow velocity from the two area's? without any velocities?
 

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