Bernoulli. Air flows from a large, pressurized tank at gage pressure, Pg.0 through a small pipe of diameter D₂ = 4 mm and exits to the atmosphere. A C-D venturi section (see Textbook fig 3.11) with throat diameter D₁ = 2mm is inserted in the pipe to measure flow rate. A U-tube manometer containing an oil (SG = 0.8) connects Dpto D, and reads an oil height of h = 6cm. What is: (a) the tank Pro and (b) the air flow rate at this P.0. Ans

Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
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Patm = 10^5, P(water) = 1000 kg/m^3 ; Pair = 1.2 kg/m^3 ; g = 9.8m/s^2
gage pressure Pg = P - Patm

**Bernoulli**

Air flows from a large, pressurized tank at gage pressure, \( P_{g,0} \), through a small pipe of diameter \( D_p = 4 \, \text{mm} \) and exits to the atmosphere. A C-D venturi section (see Textbook fig. 3.11) with throat diameter \( D_t = 2 \, \text{mm} \) is inserted in the pipe to measure flow rate. A U-tube manometer containing an oil (SG = 0.8) connects \( D_p \) to \( D_t \) and reads an oil height of \( h = 6 \, \text{cm} \). What is: (a) the tank \( P_{g,0} \) and (b) the air flow rate at this \( P_{g,0} \).

**Answer:**
(a) \( 10^1 \, \text{Pa} \); (b) \( 10^{-6} \, \text{m}^3/\text{s} \)

---

**Diagram Explanation**

The diagram on the right illustrates the setup:

- **Pipes:** It shows a horizontal pipe with diameters \( D_p \) and \( D_t \).
- **Venturi Section:** There is a narrowing in the pipe labeled with \( D_t = 2 \, \text{mm} \), representing the venturi throat.
- **Manometer:** Below the venturi is a U-tube manometer containing oil with a specific gravity \( \text{SG} = 0.8 \). The manometer indicates a height difference \( h = 6 \, \text{cm} \) between its two columns.
- **Flow Direction:** Arrows indicate the direction of airflow from the pressurized tank through the venturi and out to the atmosphere.

This setup is used to apply Bernoulli's equation for fluid dynamics to calculate the specified variables.
Transcribed Image Text:**Bernoulli** Air flows from a large, pressurized tank at gage pressure, \( P_{g,0} \), through a small pipe of diameter \( D_p = 4 \, \text{mm} \) and exits to the atmosphere. A C-D venturi section (see Textbook fig. 3.11) with throat diameter \( D_t = 2 \, \text{mm} \) is inserted in the pipe to measure flow rate. A U-tube manometer containing an oil (SG = 0.8) connects \( D_p \) to \( D_t \) and reads an oil height of \( h = 6 \, \text{cm} \). What is: (a) the tank \( P_{g,0} \) and (b) the air flow rate at this \( P_{g,0} \). **Answer:** (a) \( 10^1 \, \text{Pa} \); (b) \( 10^{-6} \, \text{m}^3/\text{s} \) --- **Diagram Explanation** The diagram on the right illustrates the setup: - **Pipes:** It shows a horizontal pipe with diameters \( D_p \) and \( D_t \). - **Venturi Section:** There is a narrowing in the pipe labeled with \( D_t = 2 \, \text{mm} \), representing the venturi throat. - **Manometer:** Below the venturi is a U-tube manometer containing oil with a specific gravity \( \text{SG} = 0.8 \). The manometer indicates a height difference \( h = 6 \, \text{cm} \) between its two columns. - **Flow Direction:** Arrows indicate the direction of airflow from the pressurized tank through the venturi and out to the atmosphere. This setup is used to apply Bernoulli's equation for fluid dynamics to calculate the specified variables.
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