solve this problem---**Question Stem:** AT WHICH POINT IS THE PRESSURE THE GREATEST? **Chart/Diagram Description:** * **Type:** Diagram illustrating fluid flow through pipes with varying cross-sections. * **Overall Layout:** The image shows three separate diagrams arranged vertically, each representing a pipe with water flowing through it. Below the diagrams is a logo and text. * **Diagram 1 (Top):** * Shows a pipe that starts with a relatively wide, circular cross-section and gradually narrows towards the right, ending with a smaller, curved opening. * A blue arrow labeled "water" points from left to right into the wider end of the pipe, indicating the direction of flow. * A black line with a perpendicular marker points to the narrow opening on the right and is labeled with a red circle containing the letter 'a'. * **Diagram 2 (Middle):** * Shows a pipe that starts with a rectangular cross-section (or possibly circular, but drawn with flat sides) and tapers down abruptly to a very narrow opening on the right. * A blue arrow labeled "water" points from left to right into the wider end of the pipe. * A black line with a perpendicular marker points to the very narrow opening on the right and is labeled with a red circle containing the letter 'b'. * **Diagram 3 (Bottom):** * Shows a pipe with a uniform circular cross-section throughout its length. * A blue arrow labeled "water" points from left to right into the left end of the pipe. * A black line with a perpendicular marker points to the right opening of the pipe and is labeled with a red circle containing the letter 'c'. * **Labels:** The points labeled are 'a', 'b', and 'c'. The flow is indicated by arrows labeled "water". * **Other Elements:** * In the bottom left corner, there is a gear-shaped logo. * Next to the logo is the text "WORLD OF ENGINEERING". **Other Relevant Text:** WORLD OF ENGINEERING

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Let's analyze three different pipe configurations to determine where fluid pressure is greatest. We have pipe A with gradual narrowing, pipe B with abrupt narrowing, and pipe C with uniform cross-section. Understanding Bernoulli's principle will help us solve this problem. Today we'll solve a fluid mechanics problem about pressure in pipes. We need to determine which of three different pipe configurations will have the greatest pressure. Understanding this requires knowledge of Bernoulli's principle and the continuity equation. Bernoulli's principle is fundamental to understanding fluid pressure. It states that as fluid velocity increases, pressure decreases. In a pipe, when fluid flows from a wide section to a narrow section, it must speed up to maintain continuity. This increased velocity results in decreased pressure at the narrow section. Let's analyze each pipe configuration. Pipe A has a gradual narrowing, which creates moderate velocity increase. Pipe B has an abrupt narrowing to a very thin opening, creating the highest velocity increase. Pipe C has uniform diameter, so velocity remains constant. According to Bernoulli's principle, higher velocity means lower pressure. The answer is Point C. In pipe C, the uniform diameter means the water velocity remains constant throughout. Since there's no velocity increase, there's no pressure decrease according to Bernoulli's principle. Pipe A has moderate velocity increase and moderate pressure decrease. Pipe B has the highest velocity increase at the narrow opening, resulting in the lowest pressure. Therefore, Point C has the greatest pressure. Let's analyze the velocity and pressure in each pipe configuration. In pipe A, the gradual narrowing causes moderate velocity increase and moderate pressure decrease. Pipe B has the most dramatic change - the abrupt narrowing creates the highest velocity increase, resulting in the lowest pressure. Pipe C maintains constant velocity throughout, so it retains the highest pressure. This demonstrates the inverse relationship between velocity and pressure in fluid flow. The final answer is Point C. Point C has the greatest pressure because the pipe has uniform diameter throughout, maintaining constant velocity. Since there's no velocity increase, there's no pressure decrease according to Bernoulli's principle. Points A and B both experience pressure drops due to velocity increases at their narrow sections, with Point B having the lowest pressure due to the most dramatic narrowing. Therefore, Point C definitively has the greatest pressure among all three configurations. Today we'll analyze a fluid mechanics problem involving three different pipe configurations. We need to determine which point has the greatest pressure when water flows through pipes with varying cross-sections. This problem demonstrates the fundamental principles of fluid dynamics, specifically Bernoulli's principle and the continuity equation. Bernoulli's principle is the foundation for solving this problem. It states that for an ideal fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant. The key insight is the inverse relationship between velocity and pressure: when fluid velocity increases, pressure decreases, and vice versa. The continuity equation is equally important for understanding this problem. It states that the mass flow rate must remain constant throughout the pipe system. This means that when the cross-sectional area decreases, the fluid velocity must increase proportionally. Conversely, in wider sections, the velocity decreases. This velocity change directly impacts pressure through Bernoulli's principle. Let's analyze each pipe configuration. Pipe A has a gradual taper, causing moderate velocity increase at the outlet. Pipe B has a very narrow constriction, creating the highest velocity increase. Pipe C maintains uniform diameter throughout, so velocity remains constant. According to Bernoulli's principle, higher velocity means lower pressure, so point C should have the highest pressure. In summary, this problem demonstrates the practical application of Bernoulli's principle and the continuity equation. When fluid flows through pipes of different cross-sections, the velocity changes inversely with the area. Higher velocities result in lower pressures. Point C, with its uniform diameter, maintains constant velocity and therefore the highest pressure. This principle is fundamental in fluid mechanics and has applications in engineering, from pipeline design to aircraft wing aerodynamics.