Chapter 19, Problem 30A

To determine

To explain: Whether more water per second will flow out the downstairs faucet than upstairs or same amount of water will flow from both the faucets.

Answer to Problem 30A

Downstairs faucet will flows out greater water than upstairs faucet.

Explanation of Solution

Introduction:

Relation between pressure and gravity is given by following equation:

  $\begin{array}{l}P=\rho gH\\ \text{Here,}\\ P\text{is pressure}\\ \rho \text{is density}\\ g\text{is gravity}\\ H\text{is height}\end{array}$

If both the faucet have equal dimensions, than more water will flow through downstairs faucet because pressure on it is greater than upstairs faucet as it is close to Earth surface. Thus, it has to travel less distance in comparison to upstairs faucet. So rate of flow of water will be greater on downstairs faucet. Also according to Pascal’s law is as depth increases pressure increases and pressure is more for downstairs faucets because depth of downstairs faucet is greater than upstairs faucet.

Conclusion:

Downstairs faucet will flows out greater water than upstairs faucet.