### Fluid Dynamics Problem**Diagram Description:**The image shows a horizontal pipe with a decreasing square cross section. It illustrates two points, A and B, along the pipe with corresponding cross-sectional areas and velocities depicted by arrows:- **Point A:** - Cross-sectional side length: \( a = 15 \, \text{cm} \) - Velocity at point A: \( v_A = 4.7 \, \text{m/s} \)- **Point B:** - Cross-sectional side length: \( b = 10 \, \text{cm} \)**Problem Statement:**An unknown fluid flows through the pipe. The goal is to determine the speed \( v_B \) of the fluid at point B. The numerical value should be entered in SI units.**Steps to Solve:**To find \( v_B \), use the principle of conservation of mass, which in the case of an incompressible fluid is expressed as:\[ A_A \times v_A = A_B \times v_B \]Where:- \( A_A \) and \( A_B \) are the cross-sectional areas at points A and B.- \( v_A \) and \( v_B \) are the velocities at points A and B.Cross-sectional area for a square is given by side\(^2\). Therefore:\[ A_A = a^2, \quad A_B = b^2 \]Substitute and solve for \( v_B \):\[ (15 \, \text{cm})^2 \times 4.7 \, \text{m/s} = (10 \, \text{cm})^2 \times v_B \]Convert cm to meters before solving:\[ (0.15 \, \text{m})^2 \times 4.7 \, \text{m/s} = (0.10 \, \text{m})^2 \times v_B \]Calculate to find \( v_B \).

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Description: ### Fluid Dynamics Problem**Diagram Description:**The image shows a horizontal pipe with a decreasing square cross section. It illustrates two points, A and B, along the pipe with corresponding cross-sectional areas and velocities depicted by arrows

Given : The velocity of the fluid at the point A is vA = 4.7 m/s and the cross-section is…

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12 point VA VB An unknown fluid flows through a horizontal pipe with a decreasing square cross section. At point A, the sides of the cross section have a length of a = 15 cm. At point B, the sides of the cross section have a length of b = 10 cm. If the speed at point A is vA = 4.7, what is the speed vR of the fluid at point B? Enter the numerical value in SI units. a Type your answer.

12 point VA VB An unknown fluid flows through a horizontal pipe with a decreasing square cross section. At point A, the sides of the cross section have a length of a = 15 cm. At point B, the sides of the cross section have a length of b = 10 cm. If the speed at point A is vA = 4.7, what is the speed vR of the fluid at point B? Enter the numerical value in SI units. a Type your answer.

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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Concept explainers

Fluid Pressure

The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.

Gauge Pressure

Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.

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Question

### Fluid Dynamics Problem

**Diagram Description:**
The image shows a horizontal pipe with a decreasing square cross section. It illustrates two points, A and B, along the pipe with corresponding cross-sectional areas and velocities depicted by arrows:

- **Point A:**
- Cross-sectional side length: \( a = 15 \, \text{cm} \)
- Velocity at point A: \( v_A = 4.7 \, \text{m/s} \)

- **Point B:**
- Cross-sectional side length: \( b = 10 \, \text{cm} \)

**Problem Statement:**
An unknown fluid flows through the pipe. The goal is to determine the speed \( v_B \) of the fluid at point B. The numerical value should be entered in SI units.

**Steps to Solve:**
To find \( v_B \), use the principle of conservation of mass, which in the case of an incompressible fluid is expressed as:
\[ A_A \times v_A = A_B \times v_B \]

Where:
- \( A_A \) and \( A_B \) are the cross-sectional areas at points A and B.
- \( v_A \) and \( v_B \) are the velocities at points A and B.

Cross-sectional area for a square is given by side\(^2\). Therefore:
\[ A_A = a^2, \quad A_B = b^2 \]

Substitute and solve for \( v_B \):
\[ (15 \, \text{cm})^2 \times 4.7 \, \text{m/s} = (10 \, \text{cm})^2 \times v_B \]

Convert cm to meters before solving:
\[ (0.15 \, \text{m})^2 \times 4.7 \, \text{m/s} = (0.10 \, \text{m})^2 \times v_B \]

Calculate to find \( v_B \).

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