What is the velocity of medicine emerging from a hypodermic syringe?

[rawimpact]

1. A hypodermic syringe contains a medicine with a density of water. The barrel of the syringe has a cross-sectional area of 2.5x10e-5 m^2. A force of 2N is exerted on the pluger (left, larger side). Determine the velocity of the medicine as it emerges from the needle

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(1) (2)=====
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2. P1 + 1/2pV1^2 + pghi = P2 + 1/2pV2^2 + pghf

Area = 2.5x10e-5 m^s, Force = 2 N

P1 = F/A = 80,000 Pascals

Because Area decreases, Velocity increases decreasing pressure so we assume P2 = 0, is this correct why we make P2 = 0?

 

[rl.bhat]

Inside the syringe pressure in the liquid is sum of atmospheric pressure and pressure due 2N force. Outside the syringe there is only atmospheric pressure.

 

[nlightner]

I would like to clarify a few things before providing a response. Firstly, the given diagram and equation do not accurately represent the situation described. The equation provided is the Bernoulli's equation, which is used to describe the conservation of energy in a fluid flow. However, it is not applicable in this situation as the medicine is not flowing through a pipe or a channel, but rather being pushed out of the syringe through a needle. Therefore, the equation cannot be used to determine the velocity of the medicine.

Secondly, the force of 2N exerted on the plunger is not a constant force. As the plunger is pushed, the force will decrease due to the decreasing cross-sectional area of the syringe barrel. This means that the velocity of the medicine will not be constant and will depend on the position of the plunger.

To determine the velocity of the medicine, we would need to consider factors such as the viscosity of the medicine, the diameter of the needle, and the length of the needle. The velocity can also be affected by external factors such as air resistance and surface tension.

In conclusion, without more information and accurate equations, it is not possible to accurately determine the velocity of the medicine emerging from a hypodermic syringe. As a scientist, it is important to consider all the relevant factors and use appropriate equations to accurately describe a situation.