Question

Plumbing usually includes air-filled tubes near water faucets, as shown in Figure 12.27. Explain why they are needed and how they work.

Short answer

Air-filled tubes create pressure difference thereby increasing the discharge.

Step-by-step solution

Concept of Poiseuille’s law.

The Poiseuille’s law defines the resistance of flow. The greater the pressure differential between two points, the greater the flow rate. The discharge through laminar flow in pipe is given by:

\[Q = \frac{{{P_2} - {P_1}}}{R}\]

Here, R is resistance of flow, Q is the discharge, P₁ and P₂ is the pressure at points 1 and 2 resp.

Explanation for use of air-filled tubes near water faucets.

Air-filled tube is used near water faucet to increase the resistance by creating a turbulence and as per Poiseuille’s law, it is clear that with increase in flow resistance discharge also increases. Therefore, air-filled tube increases the discharge through water faucet.

Due to the air-filled tube, there occurs two points with two different pressures. With this pressure difference there occurs high resistance to flow thereby increasing the discharge of flow.