A 2.0 mL syringe has an inner diameter of 6.0 mm, a needle inner diameter of 0.25 mm, 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 .

b. The nurse empties the syringe in 2.0 s. What is the flow speed of the medicine through the needle?

Question

A 2.0 mL syringe has an inner diameter of 6.0 mm, a needle inner diameter of 0.25 mm, 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 .

b. The nurse empties the syringe in 2.0 s. What is the flow speed of the medicine through the needle?

Accepted Answer

Hi, everyone in this practice problem. We're being asked to determine the speed of a hydraulic fluid when we'll have a hydraulic piston with a diameter of 4.4 or five centimeter. And a volume of 0.398 liter, it is supplied or drained of hydraulic fluid using a pipe of diameter of 1.27 centimeter. So suppose that the fluid from the piston is drained into a reservoir whose pressure is 120 millimeter mercury. And if all the fluid is sent back to the reservoir for in 2. seconds, we're being asked to determine the speed of the hydraulic fluid as it flows through the pipe. The options given are a 0.126 m per second. B, 0.4 m per seconds. C 0.4 m per second. And lastly D 1.26 m per second. So we know that the flow rate is going to be given by the equation of Q equals to V multiplied by A V is going to be the velocity of the fluid and A is going to be the cross sectional area that the fluid is going through. Therefore, we can get the speed of the hydraulic fluid as it flows through the pipe by actually just using this equation right here. So we can rearrange this, so that V will equals to Q divided by A or in this case, A will equals to pi multiplied by R squared. So V will equals to Q divided by pi R squared just like. So we want to recall that Q can be calculated by the volume divided by the time or V divided by T. And we can substitute that into our equation for V or velocity so that we get velocity equals to V divide our volume divided by pi R squared and T. So in this case, we actually have all of this information in the problem statement and we will actually um actually substitute all of this information into our equation right here for velocity. So velocity will then equals two first is going to be the volume which is given to be 0.398 liter. So 0.398 liter, we wanna convert that as well into meter cube. So it will multiply it by 10 to the power of negative three m cube divided by one liter. So that there is an si and then we want to divide this with first pi multiply that with R squared which is going to then be the diameter is given to be 1.27 centimeters. So I'm gonna write that 1.27 centimeter divided by two to get the radius. And then we want to convert that into meter. So we want to multiply that by then to the power of negative two m divided by one centimeter. And we want that in squared so squared up and multiply it by the time that it takes to send the fluid back into the reserve four, which is 2.5 seconds. In this case, calculating all of this, that will give us the velocity or the speed of the hydraulic fluid as it flows through the pipe, which will come out to be 1.26 m per second. So the speed of the hydraulic fluid is going to be 1.26 m per second and it will correspond with option D in our answer choices. So answer D will be the answer to this particular practice problem and that will be it for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics. That'll be it for this one. Thank you.

Verified Solution

Key Concepts

Flow Rate

Continuity Equation

Cross-Sectional Area