**Problem Description:**A thin stream of water flows smoothly from a faucet and falls straight down. At one point, the water is flowing at a speed of \( v_1 = 1.23 \, \text{m/s} \). At a lower point, the diameter of the stream has decreased by a factor of 0.895. What is the vertical distance \( h \) between these two points?**Answer:**\( h = \) \_\_\_\_\_\_\_\_**Explanation:**To solve for \( h \), you would typically use principles from fluid dynamics and kinematics. The conservation of mass (continuity equation) and the conservation of energy (Bernoulli's equation) are often involved.This problem requires calculating the speed at the lower point and using the change in velocity to find the vertical distance. Here are some basic steps you might consider:1. **Continuity Equation:** The flow rate must be constant, so you have: \[ A_1 v_1 = A_2 v_2 \] where \( A_1 \) and \( A_2 \) are the cross-sectional areas at the two points. If the diameter decreases by a factor of 0.895, then: \[ A_2 = (0.895)^2 A_1 \] 2. **Find \( v_2 \):** By substituting the area relationship into the continuity equation, you can solve for \( v_2 \).3. **Bernoulli’s Equation:** Relate the velocities and the height: \[ v_1^2 + 2gh_1 = v_2^2 + 2gh_2 \] Usually, you consider the difference in height (\( h = h_2 - h_1 \)) and solve for \( h \).By following these principles, you can calculate the vertical distance \( h \) as the water accelerates due to gravity.

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A thin stream of water flows smoothly from a faucet and falls straight down. At one point, the water is flowing at a speed 1.23 m/s. At a lower point, the diameter of the stream has decreased by a factor of 0.895. What is the vertical distance h between these two points? U1

A thin stream of water flows smoothly from a faucet and falls straight down. At one point, the water is flowing at a speed 1.23 m/s. At a lower point, the diameter of the stream has decreased by a factor of 0.895. What is the vertical distance h between these two points? U1

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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