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The small turbine in figure D extracts 400 W (assume efficiency equal to 1) of power from the water flow. Both pipes are commercial steel. Compute the flow rate Q in m³/hr, Why are there two solutions? Which is better? [Hint: Apply the generalized Bernoulli eq. between points (1) and (4) and then solve iteratively for Q].

The small turbine in figure D extracts 400 W (assume efficiency equal to 1) of power from the water flow. Both pipes are commercial steel. Compute the flow rate Q in m³/hr, Why are there two solutions? Which is better? [Hint: Apply the generalized Bernoulli eq. between points (1) and (4) and then solve iteratively for Q].

Introduction to Chemical Engineering Thermodynamics
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
Problem 1.1P
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### Description of Diagram The diagram consists of two main sections labeled ① and ②, illustrating the flow of fluid through a concentric cylinder system. #### Section ①: - A large tank is shown with height \( h \) and a pressure reading at the top labeled \( P_{\infty} \). - From the tank, a pipe emerges horizontally, where the interior diameter is marked as \( D_1 \). #### Section ②: - The pipe continues with an inner segment of diameter \( D_1 \) and an outer segment labelled \( D_2 \). - The length of the pipe \( L \) is 30 meters. - The flow rate of the fluid is indicated with \( Q_{\text{in, out}} \). ### Notations and Measurements - \( \rho = 1000\, \text{kg/m}^3 \): This is the density of the fluid. - \( \nu = \frac{\mu}{\rho} = 1.02 \times 10^{-6} \, \text{m}^2/\text{s} \): This is the kinematic viscosity of the fluid. - \( D_1 = 5\, \text{cm} \): Inner diameter of the outer concentric cylinder (pipe). - \( D_2 = 3\, \text{cm} \): Outer diameter of the inner cylinder. **Additional notes:** - \( D_1 \) and \( D_2 \) denote diameters related to the flow channels in the system. - The pressure \( P_{\infty} \) is shown to be consistent at the tank's surface and at the outer section in diagram ②, illustrating a closed system with no external pressure loss. This diagram can be used to analyze fluid flow dynamics in a pipe and the resulting pressure changes using principles of fluid mechanics.
Transcribed Image Text:### Description of Diagram The diagram consists of two main sections labeled ① and ②, illustrating the flow of fluid through a concentric cylinder system. #### Section ①: - A large tank is shown with height \( h \) and a pressure reading at the top labeled \( P_{\infty} \). - From the tank, a pipe emerges horizontally, where the interior diameter is marked as \( D_1 \). #### Section ②: - The pipe continues with an inner segment of diameter \( D_1 \) and an outer segment labelled \( D_2 \). - The length of the pipe \( L \) is 30 meters. - The flow rate of the fluid is indicated with \( Q_{\text{in, out}} \). ### Notations and Measurements - \( \rho = 1000\, \text{kg/m}^3 \): This is the density of the fluid. - \( \nu = \frac{\mu}{\rho} = 1.02 \times 10^{-6} \, \text{m}^2/\text{s} \): This is the kinematic viscosity of the fluid. - \( D_1 = 5\, \text{cm} \): Inner diameter of the outer concentric cylinder (pipe). - \( D_2 = 3\, \text{cm} \): Outer diameter of the inner cylinder. **Additional notes:** - \( D_1 \) and \( D_2 \) denote diameters related to the flow channels in the system. - The pressure \( P_{\infty} \) is shown to be consistent at the tank's surface and at the outer section in diagram ②, illustrating a closed system with no external pressure loss. This diagram can be used to analyze fluid flow dynamics in a pipe and the resulting pressure changes using principles of fluid mechanics.
The small turbine in figure D extracts 400 W (assume efficiency equal to 1) of power from the water flow. Both pipes are commercial steel. Compute the flow rate Q in m³/hr. Why are there two solutions? Which is better? [Hint: Apply the generalized Bernoulli equation between points (1) and (4) and then solve iteratively for Q].
Transcribed Image Text:The small turbine in figure D extracts 400 W (assume efficiency equal to 1) of power from the water flow. Both pipes are commercial steel. Compute the flow rate Q in m³/hr. Why are there two solutions? Which is better? [Hint: Apply the generalized Bernoulli equation between points (1) and (4) and then solve iteratively for Q].
Expert Solution
Step 1

Given:

ρ=1000 kg/m3ν=μρ=1.02×10-6m2sD1=0.05 mD2=0.03 m

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