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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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Momentum balance equation can be written as:
dP
:-Amv + PAū + F,→ƒ + mtotğ
dt
All terms are considered vectors, so the direction must be specified (x, y, or z). The force due to
gravity only acts along the y-direction. This equation assumes that the flow is turbulent.
Suppose fluid is flowing at steady state through a reducing pipe bend, as shown in the figure.
Turbulent flow will be assumed with frictional forces negligible. The volumetric flow rate of the
liquid and the pressure P2 at point 2 are known, as are the pipe diameters at both ends. The
vertical distance between points 1 and 2 are also known, as well as the mass of fluid inside the
bend. Derive the equations to calculate the force on the bend. Assume that the fluid density is
constant.
2)
ľ'2, P2
'L.
Rx
(a) State all assumptions
(b) Determine the velocity at point 1
(c) Determine the pressure at point 1
(d) Write the overall momentum balance. What term represents the force on the surface?
(e) Resolve the momentum balance into its x and y components
(f) Specify values for the unit vectors
(g) Simplify momentum balance equations
(h) Determine resultant force
(i) What will be the force exerted by the bend on the fluid?
Transcribed Image Text:Momentum balance equation can be written as: dP :-Amv + PAū + F,→ƒ + mtotğ dt All terms are considered vectors, so the direction must be specified (x, y, or z). The force due to gravity only acts along the y-direction. This equation assumes that the flow is turbulent. Suppose fluid is flowing at steady state through a reducing pipe bend, as shown in the figure. Turbulent flow will be assumed with frictional forces negligible. The volumetric flow rate of the liquid and the pressure P2 at point 2 are known, as are the pipe diameters at both ends. The vertical distance between points 1 and 2 are also known, as well as the mass of fluid inside the bend. Derive the equations to calculate the force on the bend. Assume that the fluid density is constant. 2) ľ'2, P2 'L. Rx (a) State all assumptions (b) Determine the velocity at point 1 (c) Determine the pressure at point 1 (d) Write the overall momentum balance. What term represents the force on the surface? (e) Resolve the momentum balance into its x and y components (f) Specify values for the unit vectors (g) Simplify momentum balance equations (h) Determine resultant force (i) What will be the force exerted by the bend on the fluid?
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