A hypodermic needle can be thought of as a large area pipe leading to a small area pipe that opens into the vein.The diameter of the plunger is 1.2 cm and the needle diameter is 0.15 cm.If the gauge pressure in the vein is 25 mmHg,what minimum force is needed on the plunger in order for a fluid flow into the vein to occur?
A)0.38 N
B)0.19 N
C)0.0060 N
D)31 N
E)0.12 N

Question

Quizplus · Accepted Answer

To find the minimum force needed on the plunger for fluid to flow into the vein, we can use Pascal's principle, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. The force needed can be calculated using the formula $F = PA$, where $F$ is the force, $P$ is the pressure, and $A$ is the area.First, convert the gauge pressure from mmHg to Pascals (Pa) since 1 mmHg = 133.322 Pa. Thus, 25 mmHg = $25 \times 133.322 = 3333.05$ Pa.The area of the plunger ($A$) can be calculated using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the plunger. The diameter of the plunger is 1.2 cm, so the radius is $0.6$ cm or $0.006$ m (since 1 cm = 0.01 m). Therefore, the area is $A = \pi (0.006)^2 = 1.13 \times 10^{-4}$ m$^2$.The minimum force needed on the plunger is then $F = PA = 3333.05 \times 1.13 \times 10^{-4} = 0.376$ N, which rounds to $0.38$ N.

A Hypodermic Needle Can Be Thought of as a Large