**Understanding Fluid Dynamics in a Pipe: A Practical Example**In this problem, piezometric tubes are tapped into a section of a pipe, as illustrated in the accompanying figure. The liquid is incompressible and flows at a volumetric flow rate of 0.35 m³/s. The piezometric head measures 1 m at the upstream location (1) and 0.5 m at the throat (2). The pipe diameter at the upstream location is 0.5 m. The challenge is to solve the following questions:*Hint: The piezometric head is the sum of the elevation and pressure heads.*(a) Determine the velocity in the upstream section.(b) Determine the velocity in the throat section.(c) Calculate the diameter in the throat section.(d) Using your findings from questions (a) and (b), qualitatively describe how pressure and velocity are related along the streamline.**Diagram Explanation:**- The diagram depicts a pipe with a constriction (throat) where measurements are taken at two different points, labeled 1 and 2.- Point 1 is located at the upstream section, and point 2 is at the narrower throat section of the pipe.- Two piezometric tubes are connected to these points, measuring the piezometric head at each location.- The velocities at these points are labeled as V₁ and V₂, respectively. Flow direction is indicated by arrows.- The datum line is referenced for elevation measurements.This exercise helps illustrate principles of fluid dynamics, specifically the relationship between velocity, pressure, and cross-sectional area in a streamlined flow, as stated by the Bernoulli equation and continuity equation in fluid mechanics.

Answered: Image /qna-images/answer/0df5d464-bbf7-47d9-869f-7875eaedcda7.jpg

Piezometric tubes are tapped into a pipe section as shown in the figure below. The liquid is incompressible and flowing at a volumetric flowrate of 0.35 m³ s-1. The piezometric head is 1 m at the upstream location (1) and 0.5 m at the throat (2). The pipe diameter at the upstream location (1) is 0.5 m. Answer the following: 1 m Flow Streamline (1) 0.5 m Datum Hint: the piezometric head is the sum of the elevation and pressure heads. (a) Find the velocity in the upstream section. (b) Find the velocity in the throat section. (c) Find the diameter in the throat section. (d) Based on your findings in (a) and (b), qualitatively describe how pressure and velocity are related along the streamline.

Piezometric tubes are tapped into a pipe section as shown in the figure below. The liquid is incompressible and flowing at a volumetric flowrate of 0.35 m³ s-1. The piezometric head is 1 m at the upstream location (1) and 0.5 m at the throat (2). The pipe diameter at the upstream location (1) is 0.5 m. Answer the following: 1 m Flow Streamline (1) 0.5 m Datum Hint: the piezometric head is the sum of the elevation and pressure heads. (a) Find the velocity in the upstream section. (b) Find the velocity in the throat section. (c) Find the diameter in the throat section. (d) Based on your findings in (a) and (b), qualitatively describe how pressure and velocity are related along the streamline.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Pressurized pipe flow

A 15-kilometer-long pipe with a pipe diameter of one meter transports water at a speed of one meter per second. The pipe has a friction coefficient of 0.005. Calculate the frictional head loss?

Question

**Understanding Fluid Dynamics in a Pipe: A Practical Example**

In this problem, piezometric tubes are tapped into a section of a pipe, as illustrated in the accompanying figure. The liquid is incompressible and flows at a volumetric flow rate of 0.35 m³/s. The piezometric head measures 1 m at the upstream location (1) and 0.5 m at the throat (2). The pipe diameter at the upstream location is 0.5 m. The challenge is to solve the following questions:

*Hint: The piezometric head is the sum of the elevation and pressure heads.*

(a) Determine the velocity in the upstream section.

(b) Determine the velocity in the throat section.

(c) Calculate the diameter in the throat section.

(d) Using your findings from questions (a) and (b), qualitatively describe how pressure and velocity are related along the streamline.

**Diagram Explanation:**

- The diagram depicts a pipe with a constriction (throat) where measurements are taken at two different points, labeled 1 and 2.
- Point 1 is located at the upstream section, and point 2 is at the narrower throat section of the pipe.
- Two piezometric tubes are connected to these points, measuring the piezometric head at each location.
- The velocities at these points are labeled as V₁ and V₂, respectively. Flow direction is indicated by arrows.
- The datum line is referenced for elevation measurements.

This exercise helps illustrate principles of fluid dynamics, specifically the relationship between velocity, pressure, and cross-sectional area in a streamlined flow, as stated by the Bernoulli equation and continuity equation in fluid mechanics.

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