Water is traveling through a horizontal pipe with a speed of 1.9 m/s and at a pressure of 200 kPa. This pipe is reduced to a new pipe which has a diameter half that of the first section of pipe. Determine the speed and pressure of the water in the new, reduced in size pipe. (a) speed m/s (b) pressure |kPa

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

Water is traveling through a horizontal pipe with a speed of 1.9 m/s and at a pressure of 200 kPa. This pipe is reduced to a new pipe which has a diameter half that of the first section of pipe. Determine the speed and pressure of the water in the new, reduced in size pipe.

**Questions:**

(a) Speed  
[           ] m/s

(b) Pressure  
[           ] kPa

**Explanation:**

This problem involves fluid dynamics, specifically the principles of continuity and Bernoulli's equation. The continuity equation will help determine the speed of the water in the reduced pipe, while Bernoulli’s equation will help find the pressure. The key concepts to apply here are:

1. **Continuity Equation:** \( A_1V_1 = A_2V_2 \)
   - Where \( A \) is the cross-sectional area of the pipe, and \( V \) is the velocity of the fluid.

2. **Bernoulli's Equation:** \( P_1 + \frac{1}{2}\rho V_1^2 = P_2 + \frac{1}{2}\rho V_2^2 \)
   - Where \( P \) is the pressure, \( \rho \) is the fluid density, and \( V \) is velocity.
Transcribed Image Text:**Problem Statement:** Water is traveling through a horizontal pipe with a speed of 1.9 m/s and at a pressure of 200 kPa. This pipe is reduced to a new pipe which has a diameter half that of the first section of pipe. Determine the speed and pressure of the water in the new, reduced in size pipe. **Questions:** (a) Speed [           ] m/s (b) Pressure [           ] kPa **Explanation:** This problem involves fluid dynamics, specifically the principles of continuity and Bernoulli's equation. The continuity equation will help determine the speed of the water in the reduced pipe, while Bernoulli’s equation will help find the pressure. The key concepts to apply here are: 1. **Continuity Equation:** \( A_1V_1 = A_2V_2 \) - Where \( A \) is the cross-sectional area of the pipe, and \( V \) is the velocity of the fluid. 2. **Bernoulli's Equation:** \( P_1 + \frac{1}{2}\rho V_1^2 = P_2 + \frac{1}{2}\rho V_2^2 \) - Where \( P \) is the pressure, \( \rho \) is the fluid density, and \( V \) is velocity.
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