Question

A 5.0 mL syringe has an inner diameter of 6.0 mm , a needle inner diameter of 0.69 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's vein and so has to push against the patient's blood pressure which is 140 over 100. The nurse empties the syringe in 2.9 s . What is the flow speed of the medicine through the needle and into the vein?

Answer 1

To calculate the flow speed of the medicine, use the equation for flow rate and substitute the given values.

Step-by-step explanation:

To calculate the flow speed of the medicine through the needle and into the vein, we can use the equation for flow rate. The flow rate is equal to the volume of the medicine divided by the time it takes to empty the syringe. The volume of the medicine can be found by subtracting the volume of the empty syringe from the initial volume of the syringe.

Let's assume that the initial volume of the syringe is V. The volume of the medicine is V - 5.0 mL. Since the nurse empties the syringe in 2.9 s, the flow rate can be calculated as (V - 5.0 mL) / 2.9 s.

Using the given values for the syringe dimensions and the blood pressure, you can substitute these values into the equation to find the flow speed of the medicine through the needle and into the vein.

Answer 2

To calculate the flow speed of the medicine, we need the volume of the syringe divided by the time taken to empty it. The cross-sectional area of the needle is also required to determine the flow velocity. However, some essential information is missing to complete the calculation.

Step-by-step explanation:

To calculate the flow speed of the medicine through the needle and into the vein, we need to consider the volume of the syringe and the time taken to empty it. The volume of the syringe is given as 5.0 mL and the time taken is 2.9 seconds.

To find the flow speed, V, we use the formula:

V = Volume / Time

First convert the volume from milliliters to cubic meters (since milliliters are not a standard SI unit), then divide by the time to find the flow speed in meters per second (m/s).

Next, using the needle's inner diameter, we can find its cross-sectional area, A, with the formula:

A = π * (d/2)^2

Where d is the diameter of the needle. With the cross-sectional area and the flow speed, we can calculate the velocity of the fluid through the needle.

Unfortunately, there is not enough information provided to complete the calculation. Specifically, we are not given the relationship between the pressure the nurse pushes against and how that translates to flow speed through the syringe's needle.