Need help with horizontal syringe Bernoulli's Principle problem.

In summary, Bernoulli's Principle states that as the speed of a fluid increases, the pressure decreases. It can be applied to various situations, such as the flow of fluids through pipes and the lift of an airplane wing. In a horizontal syringe, the principle explains how the fluid is pushed out by the plunger due to the decrease in pressure caused by an increase in speed. However, this principle assumes that the fluid is incompressible, which may not always be the case in real-world situations. To solve problems involving Bernoulli's Principle in a horizontal syringe, one must consider the initial and final positions of the plunger, as well as the volume and density of the fluid. Some examples of real-world applications of
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Homework Statement
Dr. Jane is ready to inject medicine into Bob. The hypodermic syringe she uses contains a medicine with the same density as water. The barrel of the syringe has a cross-sectional area of 2.50 x 10^-5 m^2. The cross-sectional area of the needle is 1.0 x 10^-8 m^2. In the absence of a force on the plunger, the pressure everywhere is atmospheric pressure. A 2.0 N force is exerted on the plunger, making medicine squirt from the needle to insure there is no air in the needle prior to giving the shot. Determine the speed of the emerging fluid. Assume that the pressure in the needle remains at atmospheric pressure, that the syringe is horizontal, and the speed of the emerging fluid is the same as the speed of the fluid in the needle.
Relevant Equations
(P1) + ρg(y1) + 0.5ρ(v1)^2 = (P2) + ρg(y2) + 0.5ρ(v2)^2
P=F/A
(A1)(v1) = (A2)(v2)
Untitled drawing.png


Did I do this problem correctly? I felt like I did this wrong because the answer is suppose to be around 50 m/s.
 
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  • #2
Your work and answer look correct to me.
 
  • #3
TSny said:
Your work and answer look correct to me.
Thx
 

1. How does Bernoulli's Principle apply to a horizontal syringe?

Bernoulli's Principle states that as the speed of a fluid increases, its pressure decreases. In the case of a horizontal syringe, the fluid (usually air or water) is forced through a smaller opening, causing it to speed up and decrease in pressure.

2. Why is Bernoulli's Principle important in this situation?

In a horizontal syringe, Bernoulli's Principle helps to explain why the fluid is able to flow through the smaller opening. Without this principle, the fluid would not be able to overcome the resistance of the smaller opening and flow through it.

3. How does the force of the fluid change as it moves through the horizontal syringe?

As the fluid moves through the smaller opening, its speed increases and its pressure decreases. This results in a decrease in the force exerted by the fluid, which is why the plunger is able to be pushed down with less effort.

4. Can Bernoulli's Principle be applied to other situations besides a horizontal syringe?

Yes, Bernoulli's Principle can be applied to any situation where a fluid is forced through a smaller opening or over a curved surface. It is commonly used to explain the lift force on airplane wings and the flow of water through pipes.

5. Are there any limitations to Bernoulli's Principle?

While Bernoulli's Principle is a useful tool for understanding fluid dynamics, it is not a universal law and has its limitations. It assumes that the fluid is incompressible, non-viscous, and that there is no energy loss due to friction. In real-world situations, these assumptions may not hold true and the effects of Bernoulli's Principle may be less pronounced or even reversed.

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