The pressure of water pipe when tap is open and closed are 3  105 N m-2and 3·5  105 N m-2 respectively. Withopen tap, the velocity of water flowing is,

1. ### Break Down the Problem

1. Calculate the difference in pressure between the open tap and closed tap conditions.
2. Use Bernoulli's equation to find the velocity of water flowing when the tap is open.

2. ### Relevant Concepts

• The pressure difference can be used in Bernoulli's equation, where the velocity $v$ of a fluid can be calculated from the pressure difference $\Delta P$: $\Delta P = \frac{1}{2} \rho v^2$ where:
  • $\Delta P$ is the pressure difference,
  • $\rho$ is the density of water (typically $1000 \text{ kg/m}^3$),
  • $v$ is the velocity of water.

3. ### Analysis and Detail

1. Calculate Pressure Difference: $\Delta P = P_{\text{closed}} - P_{\text{open}} = 3.5 \times 10^5 \, \text{N/m}^2 - 3 \times 10^5 \, \text{N/m}^2 = 0.5 \times 10^5 \, \text{N/m}^2$

2. Substitute into Bernoulli's equation to find v: $0.5 \times 10^5 = \frac{1}{2} \times 1000 \times v^2$ $0.5 \times 10^5 = 500 v^2$ $v^2 = \frac{0.5 \times 10^5}{500}$ $v^2 = 100 \implies v = \sqrt{100} = 10 \, \text{m/s}$

4. ### Verify and Summarize

• The calculations have been verified step by step. The pressure difference and subsequent calculations align correctly with Bernoulli's principle.

Final Answer

The velocity of water flowing when the tap is open is $10 \, \text{m/s}$.