A hypodermic syringe (see Fig. P 5.30 ) is used to apply a...

A hypodermic syringe (see Fig. $P 5.30$ ) is used to apply a vaccine. If the plunger is moved forward at the steady rate of $20 \mathrm{mm} / \mathrm{s}$ and if vaccine leaks past the plunger at 0.1 of the volume flowrate out the needle opening, calculate the average velocity of the needle exit flow. The inside diameters of the syringe ard the needle are $20 \mathrm{mm}$ and $0.7 \mathrm{mm}$

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Key Concepts

Cross-Sectional Area Calculation

Determining the cross-sectional area of a circular conduit is essential in fluid flow problems. The area is computed using the formula based on the diameter (or radius) of the circle, which directly affects the flow rate and velocity of the fluid.

Continuity Equation

The continuity equation is a fundamental principle in fluid mechanics stating that for an incompressible fluid, the product of cross-sectional area and velocity remains constant along a streamline. This ensures that if the area decreases in one part of the system, the velocity must increase correspondingly, and vice versa.

Volume Flow Rate

The volume flow rate represents the quantity of fluid passing through a given cross-sectional area per unit time. It is calculated as the product of the cross-sectional area and the fluid velocity, and is a key parameter in analyzing and designing fluid systems.

Conservation of Mass

Conservation of mass in fluid flow means that the mass of the fluid remains constant when moving through a system without addition or loss. This principle is applied to relate different flow speeds through changes in the cross-sectional areas, ensuring that any leakage or loss is appropriately accounted for in the overall balance.

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