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A fluid flows past a circular cylinder of radius a with an upstream speed of Vo...
7. A fluid flows past a sphere with an upstream velocity of Vo = 40 m/s...
7. A fluid flows past a sphere with an upstream velocity of Vo = 40 m/s as shown in the figure below. From a more advanced theory, it is found that the speed of the fluid along the front part of the sphere is V = (3/2)Vo sin 0. 40° VO, - r oka (a) Determine the streamwise and normal components of the acceleration at point A if the radius of the sphere is a = 0.20 m. (b) Find...
1. Inviscid incompressible fluid pass a cylinder having a radius of R as shown in the...
1. Inviscid incompressible fluid pass a cylinder having a radius of R as shown in the figure below. The fluid velocity along the dividing streamline is found to be V = V, (1-R /x) a) Determine the pressure gradient (ap/ ôx) along the streamline b) Obtain the pressure p(x) for - sxs-R c) Plot the pressure distribution froma distance 15 m ahead of the cylinder to the stagnation point for flow speeds of Vo 0, 10 km/hr and 20 km/hr...
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1. The figure below shows the streamlines for the flow past a spinning circular cylinder. In the cylindrical coo...
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1. The figure below shows the streamlines for the flow past a spinning circular cylinder. In the cylindrical coordinates, the stream function can be written as ψ Uosine (r-7/-Kln (5). where R is the radius of the cylinder. Assuming that the pressure in the far upstream is po. find the pressure distribution on the surface.
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1....
3. An incompressible, viscous fluid with density, p, flows past a solid flat plate which has...
3. An incompressible, viscous fluid with density, p, flows past a solid flat plate which has a depth, b, into the page. The flow initially has a uniform velocity U., before contacting the plate. After contact with the plate at a distance x downstream from the leading edge, the flow velocity profile is altered due to the no-slip condition. The velocity profile at location x is approximated to have a linear shape, u = U. z for y s 8...
Problem 1 An incompressible, viscous fluid with density, p, flows past a solid flat plate which...
Problem 1 An incompressible, viscous fluid with density, p, flows past a solid flat plate which has a width, b, into the page. The flow initially has a uniform velocity U before contacting the plate. The velocity profile at location x is estimated to have a parabolic shape, u-u[(Y)-(,)21"for ysiand u-vfor y 20 where isthe boundary layer thickness. (a) Determine the upstream height from the plate, h, of a streamline which has a height, 6, at the downstream location, x....
Fluid shown in (Figure 1) flows through the curved pipe such that fluid particles move along...
Fluid shown in (Figure 1) flows through the curved
pipe such that fluid particles move along the center streamline
with the velocity of V=(14s^2 + 1000t^3/2 +4)m/s, where s is in
meters and t is in seconds
Part A
Determine the magnitude of the acceleration of a particle at point
A, where s= 0.3m, if it arrives t = 0.02s
a=
Fundamental Problem 3.8 Fluid shown in (Figure 1) flows through the curved pipe Y Pa such that fluid particles...
Problem 3: ter with density #1000k/m3 is flowing around a cylinder submergedinto a river. The riv...
Problem 3: ter with density #1000k/m3 is flowing around a cylinder submergedinto a river. The river velocity is given by U-5 m/s and the cylinder radius is R -1.5 m. Calculate the pressure difference between point So (stagnation point) and the point S located at 45° on the surface. Note that as per the inviscid potential flow theory, the velocity at the external surface of the cylinder is given by v,--2U sin . Use g 9.81 m/s2 for gravity U...
Consider a circular cylinder of radius a whose central axis is stationary. The cylinder is surrounded by a fluid that i...
Consider a circular cylinder of radius a whose central axis is stationary. The cylinder is surrounded by a fluid that is moving with a uniform steady velocity Uk far from the cylinder; the cylinder axis is in the z-direction The cylinder is also spinning on its axis with constant angular velocity, Ω2, where x, у and z are the usual Cartesian unit vectors We wish to model this 2D flow using an inviscid approximation. This is achieved by first calculating...
The small block P travels with constant speed v = 1.70 m/s in the circular path...
The small block P travels with constant speed v = 1.70 m/s in the circular path of radius r = 1.32 m on the inclined surface. If 0 = 0 at time t = 0, determine the x-, y, and z-components of velocity and acceleration at time t = 2.1 s. Answers: At t = 2.1 s -0.072097 m/s, ax = i -1.9656 m/s2 1.698106 m/s, ay = -0.10331 m/s2 0.035164 m/s, a, = 0.958695573 m/s2 N
Now evaluate the mass and momentum into and out of the CV shown with 1.0s y Rs 1.5 at (2) Let p 1...
Now evaluate the mass and momentum into and out of the CV shown with 1.0s y Rs 1.5 at (2) Let p 1200 kg/m2, Uoo- 20 m/s and cylinder radius R 0.01 m 1 cm and Az 1 m Note: The flow does not cross streamlines, so there is no flow across the side boundaries. Exit (2) NO SCALE Variable u vs y at x2-0 Inlet (1) y- H1 and v 0 constant u Uo constant v0 A) Find mass...
7. A fluid flows past a sphere with an upstream velocity of Vo = 40 m/s as shown in the figure below. From a more advanced theory, it is found that the speed of the fluid along the front part of the sphere is V = (3/2)Vo sin 0. 40° VO, - r oka (a) Determine the streamwise and normal components of the acceleration at point A if the radius of the sphere is a = 0.20 m. (b) Find...
1. Inviscid incompressible fluid pass a cylinder having a radius of R as shown in the figure below. The fluid velocity along the dividing streamline is found to be V = V, (1-R /x) a) Determine the pressure gradient (ap/ ôx) along the streamline b) Obtain the pressure p(x) for - sxs-R c) Plot the pressure distribution froma distance 15 m ahead of the cylinder to the stagnation point for flow speeds of Vo 0, 10 km/hr and 20 km/hr...
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1. The figure below shows the streamlines for the flow past a spinning circular cylinder. In the cylindrical coordinates, the stream function can be written as ψ Uosine (r-7/-Kln (5). where R is the radius of the cylinder. Assuming that the pressure in the far upstream is po. find the pressure distribution on the surface.
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1....
3. An incompressible, viscous fluid with density, p, flows past a solid flat plate which has a depth, b, into the page. The flow initially has a uniform velocity U., before contacting the plate. After contact with the plate at a distance x downstream from the leading edge, the flow velocity profile is altered due to the no-slip condition. The velocity profile at location x is approximated to have a linear shape, u = U. z for y s 8...
Problem 1 An incompressible, viscous fluid with density, p, flows past a solid flat plate which has a width, b, into the page. The flow initially has a uniform velocity U before contacting the plate. The velocity profile at location x is estimated to have a parabolic shape, u-u[(Y)-(,)21"for ysiand u-vfor y 20 where isthe boundary layer thickness. (a) Determine the upstream height from the plate, h, of a streamline which has a height, 6, at the downstream location, x....
Fluid shown in (Figure 1) flows through the curved
pipe such that fluid particles move along the center streamline
with the velocity of V=(14s^2 + 1000t^3/2 +4)m/s, where s is in
meters and t is in seconds
Part A
Determine the magnitude of the acceleration of a particle at point
A, where s= 0.3m, if it arrives t = 0.02s
a=
Fundamental Problem 3.8 Fluid shown in (Figure 1) flows through the curved pipe Y Pa such that fluid particles...
Problem 3: ter with density #1000k/m3 is flowing around a cylinder submergedinto a river. The river velocity is given by U-5 m/s and the cylinder radius is R -1.5 m. Calculate the pressure difference between point So (stagnation point) and the point S located at 45° on the surface. Note that as per the inviscid potential flow theory, the velocity at the external surface of the cylinder is given by v,--2U sin . Use g 9.81 m/s2 for gravity U...
Consider a circular cylinder of radius a whose central axis is stationary. The cylinder is surrounded by a fluid that is moving with a uniform steady velocity Uk far from the cylinder; the cylinder axis is in the z-direction The cylinder is also spinning on its axis with constant angular velocity, Ω2, where x, у and z are the usual Cartesian unit vectors We wish to model this 2D flow using an inviscid approximation. This is achieved by first calculating...
The small block P travels with constant speed v = 1.70 m/s in the circular path of radius r = 1.32 m on the inclined surface. If 0 = 0 at time t = 0, determine the x-, y, and z-components of velocity and acceleration at time t = 2.1 s. Answers: At t = 2.1 s -0.072097 m/s, ax = i -1.9656 m/s2 1.698106 m/s, ay = -0.10331 m/s2 0.035164 m/s, a, = 0.958695573 m/s2 N
Now evaluate the mass and momentum into and out of the CV shown with 1.0s y Rs 1.5 at (2) Let p 1200 kg/m2, Uoo- 20 m/s and cylinder radius R 0.01 m 1 cm and Az 1 m Note: The flow does not cross streamlines, so there is no flow across the side boundaries. Exit (2) NO SCALE Variable u vs y at x2-0 Inlet (1) y- H1 and v 0 constant u Uo constant v0 A) Find mass...
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