Homework Answers
1. True, in general newtonian fluid is assumed to be incompressible.
2. False, speed of sound through fluid depends on Pressure, temperature, and density.
3. True, by definition incompressible fluid has negligible change in density.
4. False, incompressibiliy does not depend on pressure
5. True, If there is no accumulation of mass. Conservation of mass equation is applicable.
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A Newtonian fluid is, by definition, also incompressible. The speed of sound...
1. One of the fundamental equations in fluid flow is the equation of discontinuity. A. True...
1. One of the fundamental equations in fluid flow is the equation of discontinuity. A. True B. False 2. What is the equation for conservation of flow rate of an incompressible fluid through various cross sections of tube? This fluid has a speed of through a cross section and the speed of through a cross section . A. B. 3. Now there is water running through a tube with two cross sections, =2 meter^2 and = 5 meter^2. Known that...
An incompressible Newtonian fluid flow through a horizontal circular tube is shown in the following figure....
An incompressible Newtonian fluid flow through a horizontal circular tube is shown in the following figure. We assume that the flow is steady, and its direction is parallel to the wall. By using the Navier-Stokes equations. determine the velocity profile and calculate the mean velocity and maximum velocity; Please give the details about how to simplify the N-S equation, how to integrate the simplified N-S equations with the proper boundary conditions, and the relationship between the mean velocity and maximum...
Advanced Fluid Mechanics For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters)...
Advanced Fluid Mechanics
For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters) )= Vp - Vgx + V xu at and whether or not the fluid is incompressible, we also have the conservation of mass Dp +pv u 0. Dt Show that x Vp Dt Deduce that, if p is a function of palone, the vorticity equation is exactly as in the incompressible, constant density case, except that ois replaced by ap.
For an inviscid...
e) Write down: i) the equation for mass conservation for an incompressible fluid flowing through a...
e) Write down: i) the equation for mass conservation for an incompressible fluid flowing through a tube of varying diameter, and ii) Bernoulli's equation. iii) Water is supplied to a house through an inlet pipe having an internal diameter of 40 mm. A pipe of internal diameter 20 mm delivers water to an upper level, 5.5 m above the inlet pipe at a rate of 4 L/min. and a pressure of 2 atm. Calculate the pressure of the water at...
10. Immiscible fluids Two immiscible incompressible Newtonian fluids flow together through in thedirection two lates separated...
10. Immiscible fluids Two immiscible incompressible Newtonian fluids flow together through in thedirection two lates separated by a distance H in the y-direction. Let us make thé top plate /move with ection while fixing the bottom plate. At steady state, however, there be a little slip velocity of the more dense fluid only at the lower boundary The flow constant vetocity V in the x-dir is ynidirectional and faminar. For convenience, we take that x is the flow direction and...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is such that water flows through a pipe, exhibiting a laminar and steady-state flow. At the top end of the pipe, the flow tube has a cross-sectional area A and point 1 (located on the central streamline) is exposed to the ambient environment. The pipe drops through a A vertical distance h7 while its area decreases to when it reaches point 2 (also on the...
True (T) or false (F) statements (10/100). i. The Reynolds Transport Theorem is a general equation...
True (T) or false (F) statements (10/100). i. The Reynolds Transport Theorem is a general equation valid for steady, insteady, uniform non-uniform, compressible and incompressible flows. ii. If the temperature of a fluid increases then its viscosity decreases iii. Unlike the Bernoulli equation, Euler's equation applies to both the steady and unsteady flows iv. Under non-uniform steady-state conditions, the piezometric pressure approaches the stagnation pressure in the areas with higher velocity. v. Physical behavior of liquids differs from solids in...
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below....
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below. An identical fluid is injected at a constant speed V through the bottom plate and simultaneously extracted from the upper plate at the same velocity. There is no gravity force in x and y directions (g-g,-0). Assume the flow to be steady, fully-developed, 2D, and the pressure gradient in the x direction to be a constant P = constant). (a) Write the continuity equation...
Question 1: True or false. The no-slip boundary condition is only used in steady state problems....
Question 1: True or false. The no-slip boundary condition is only used in steady state problems. Question 2: Express in words the equation for conservation of mass for a pure fluid. Question 3: The shear stress required to detach endothelial cells in vitro is 26 Pa. A surgeon has invented a catheter that can rotate once inside arteries. The idea of the catheter is to exert shear stresses such that cells lining the artery are detached and the vessel ‘cleaned...
The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the...
The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the incompressible limit, the density of the fluid may be regarded as a constant, and the system of equations becomes, Because of the non-linearities, there are very few exact solutions that are known for these equations. One of the exact solutions is pressure-driven channel (or pipe) flow, also known as Poiseuille flow. In this flow, all solid, no-slip walls are parallel to the x-axis, and...
An incompressible Newtonian fluid flow through a horizontal circular tube is shown in the following figure. We assume that the flow is steady, and its direction is parallel to the wall. By using the Navier-Stokes equations. determine the velocity profile and calculate the mean velocity and maximum velocity; Please give the details about how to simplify the N-S equation, how to integrate the simplified N-S equations with the proper boundary conditions, and the relationship between the mean velocity and maximum...
Advanced Fluid Mechanics
For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters) )= Vp - Vgx + V xu at and whether or not the fluid is incompressible, we also have the conservation of mass Dp +pv u 0. Dt Show that x Vp Dt Deduce that, if p is a function of palone, the vorticity equation is exactly as in the incompressible, constant density case, except that ois replaced by ap.
For an inviscid...
e) Write down: i) the equation for mass conservation for an incompressible fluid flowing through a tube of varying diameter, and ii) Bernoulli's equation. iii) Water is supplied to a house through an inlet pipe having an internal diameter of 40 mm. A pipe of internal diameter 20 mm delivers water to an upper level, 5.5 m above the inlet pipe at a rate of 4 L/min. and a pressure of 2 atm. Calculate the pressure of the water at...
10. Immiscible fluids Two immiscible incompressible Newtonian fluids flow together through in thedirection two lates separated by a distance H in the y-direction. Let us make thé top plate /move with ection while fixing the bottom plate. At steady state, however, there be a little slip velocity of the more dense fluid only at the lower boundary The flow constant vetocity V in the x-dir is ynidirectional and faminar. For convenience, we take that x is the flow direction and...
Water can be considered as a non-viscous incompressible fluid of density p. A laboratory set-up is such that water flows through a pipe, exhibiting a laminar and steady-state flow. At the top end of the pipe, the flow tube has a cross-sectional area A and point 1 (located on the central streamline) is exposed to the ambient environment. The pipe drops through a A vertical distance h7 while its area decreases to when it reaches point 2 (also on the...
True (T) or false (F) statements (10/100). i. The Reynolds Transport Theorem is a general equation valid for steady, insteady, uniform non-uniform, compressible and incompressible flows. ii. If the temperature of a fluid increases then its viscosity decreases iii. Unlike the Bernoulli equation, Euler's equation applies to both the steady and unsteady flows iv. Under non-uniform steady-state conditions, the piezometric pressure approaches the stagnation pressure in the areas with higher velocity. v. Physical behavior of liquids differs from solids in...
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below. An identical fluid is injected at a constant speed V through the bottom plate and simultaneously extracted from the upper plate at the same velocity. There is no gravity force in x and y directions (g-g,-0). Assume the flow to be steady, fully-developed, 2D, and the pressure gradient in the x direction to be a constant P = constant). (a) Write the continuity equation...
The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the incompressible limit, the density of the fluid may be regarded as a constant, and the system of equations becomes, Because of the non-linearities, there are very few exact solutions that are known for these equations. One of the exact solutions is pressure-driven channel (or pipe) flow, also known as Poiseuille flow. In this flow, all solid, no-slip walls are parallel to the x-axis, and...
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