**Problem Statement:**A liquid is flowing through a horizontal pipe whose radius is 0.0267 m. The pipe bends straight upward through a height of 14.0 m and joins another horizontal pipe whose radius is 0.0870 m. What volume flow rate will keep the pressures in the two horizontal pipes the same?**Diagram Explanation:**The diagram illustrates a pipe system where:1. The first horizontal pipe has a radius denoted as \( r_1 \). Its diameter is labeled \( 2r_1 \), and it shows a flow velocity \( v_1 \) in the horizontal direction.2. The pipe bends vertically upward to a height \( h = 14.0 \, \text{m} \).3. After ascending, the pipe connects to a second horizontal pipe with a radius \( r_2 \). Its diameter is represented as \( 2r_2 \), and it has a flow velocity \( v_2 \).**Input Interface:**- A field labeled "Number" is present for entering the calculated volume flow rate.- Units are selectable, with the default set to cubic meters per second (m³/s).

Horizontal pipe radii, Pipe bent height, Another horizontal pipe radii, to find volume flow rate which keeps pressures same in two horizontal pipes.continuity equation : The total volume of the fluid entering the pipe is equal to the sum of the total volume of the fluid leaving the pipe and the volume of fluid held back inside the pipe. ---------------------(1) eqBernoullis equation: -----------------------(2) eqp = pressurev= velocityg= acceleration due to gravityh = heightUsing Bernoullis theorem from (2) eq as distance of pipe from ground is 0.pressure in the two horizontal pipes is same i.e ------------------(3) equsing equation of continuityfrom equation (1) ----------------------(4)putting (4) equation in (2) equationand flow rate volume flow rate that keeps the pressures same in two horizontal pipes is

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A liquid is flowing through a horizontal pipe whose radius is 0.0267 m. The pipe bends straight upward through a height of 14.0 m and joins another horizontal pipe whose radius is 0.0870 m. What volume flow rate will keep the pressures in the two horizontal pipes the same? Number 2r1 i V1 h ! Units 202 m^3/s <

A liquid is flowing through a horizontal pipe whose radius is 0.0267 m. The pipe bends straight upward through a height of 14.0 m and joins another horizontal pipe whose radius is 0.0870 m. What volume flow rate will keep the pressures in the two horizontal pipes the same? Number 2r1 i V1 h ! Units 202 m^3/s <

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter14: Fluid Mechanics

Section: Chapter Questions

Problem 14.16OQ: An ideal fluid flows through a horizontal pipe whose diameter varies along its length. Measurements...

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Concept explainers

Variation of pressure

From the equation of pressure, pressure is directly proportional to the applied force.

Question

**Problem Statement:**

A liquid is flowing through a horizontal pipe whose radius is 0.0267 m. The pipe bends straight upward through a height of 14.0 m and joins another horizontal pipe whose radius is 0.0870 m. What volume flow rate will keep the pressures in the two horizontal pipes the same?

**Diagram Explanation:**

The diagram illustrates a pipe system where:

1. The first horizontal pipe has a radius denoted as \( r_1 \). Its diameter is labeled \( 2r_1 \), and it shows a flow velocity \( v_1 \) in the horizontal direction.
2. The pipe bends vertically upward to a height \( h = 14.0 \, \text{m} \).
3. After ascending, the pipe connects to a second horizontal pipe with a radius \( r_2 \). Its diameter is represented as \( 2r_2 \), and it has a flow velocity \( v_2 \).

**Input Interface:**

- A field labeled "Number" is present for entering the calculated volume flow rate.
- Units are selectable, with the default set to cubic meters per second (m³/s).

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