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2. Consider an incompressible flow around a semi-cylinder as shown in figure 3. Assume the velocity...
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...
QUESTION 2 (14 marks) Explain how to form a steady uniform flow around a cylinder based on superp...
QUESTION 2 (14 marks) Explain how to form a steady uniform flow around a cylinder based on superposition (6 marks) (a) of several basic potential flows. (b) Based on the surface pressure distribution of the flow around the cylinder in (a) explain why the theoretical pressure distribution as illustrated in Fig. 1 is different (8 marks) from the corresponding experimental results. 3 Experimental Theoretical (inviscid) -3 0 30 60 90 120 150 180 β (deg) Figure 1
QUESTION 2 (14...
QUESTION 2 In an experiment to measure approaching uniform flow, U.to a non-rotating circular cylinder as...
QUESTION 2 In an experiment to measure approaching uniform flow, U.to a non-rotating circular cylinder as shown in Figure Q2, a small hole is to be drilled at the stagnation point on the cylinder surface. (a) Determine the location of the drilled hole on the cylinder surface using potential flow theory by combining a doublet with a uniform flow. (3.5 marks) (b) Determine the theoretical pressure distribution expression on the cylinder surface, Pc and plot or sketch a graph of...
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...
4. Air flows around a flat-bottomed airfoil shown in the figure. The air velocity at the...
4. Air flows around a flat-bottomed airfoil shown in the figure. The air velocity at the edge of the boundary layer at the bottom is the free stream velocity, U, and at the top it is u(x). Determine the lift coefficient, CL , for this flow if u²(x) = U u = ulx) P, u(x) U pol
(3) As shown in the figure below, wind blows at a uniform, constant velocity of 60...
(3) As shown in the figure below, wind blows at a uniform, constant velocity of 60 mph over a six foot diameter, air- tight Quonset hut is located on a flat plain. Assume 2d, inviscid, irrotational flow and that the density of the air is 0.002 slug/ft? Voo a. Where on the surface of the hut should the vent A be located so that the pressure inside the hut is equal to P? b. Find the difference in static pressure...
QUESTION 3 (14 marks) Variation in drag cylinder is shown in Figure 2 (a) At point coefficient (C...
QUESTION 3 (14 marks) Variation in drag cylinder is shown in Figure 2 (a) At point coefficient (CD) against Reynolds number (Re) for flow around a smooth a, point out whether drag is mainly contributed by pressure drag or friction (8 marks) drag, and explain the reason why (6 marks) (b) Explain the reason why there is a sudden drop in Co at point 400 200 100 40 20 10 60 N C, 6 Smoath cylinder 0.6 0.4 0.2 0.1...
3. Velocity profiles are measured at the upstream end (surface I) and at the downstream end...
3. Velocity profiles are measured at the upstream end (surface I) and at the downstream end (surface 2) of the control volume shown in figure below. Surfaces 3 and 4 are streamlines. If the flow is incompressible, two dimensional, and steady, what is the drag coefficient for the airfoil? The vertical dimension Hp = 0.025c. The pressure is Pao (a constant) over the entire surface of the control volume. Streamline (--v-(1-05000 )
2. Water flows over a flat surface at 8 m/s, as shown in figure. A pump...
2. Water flows over a flat surface at 8 m/s, as shown in figure. A pump draws off water through a narrow slit at a volume rate of 0.2 m2/s per meter length of the slit. Assume that the fluid is incompressible and inviscid and can be represented by the combination of a uniform flow and a sink. a) Based on method of superposition, propose a general expression for stream function ψ velocity potential ф, and velocity components of v,...
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...
QUESTION 2 (14 marks) Explain how to form a steady uniform flow around a cylinder based on superposition (6 marks) (a) of several basic potential flows. (b) Based on the surface pressure distribution of the flow around the cylinder in (a) explain why the theoretical pressure distribution as illustrated in Fig. 1 is different (8 marks) from the corresponding experimental results. 3 Experimental Theoretical (inviscid) -3 0 30 60 90 120 150 180 β (deg) Figure 1
QUESTION 2 (14...
QUESTION 2 In an experiment to measure approaching uniform flow, U.to a non-rotating circular cylinder as shown in Figure Q2, a small hole is to be drilled at the stagnation point on the cylinder surface. (a) Determine the location of the drilled hole on the cylinder surface using potential flow theory by combining a doublet with a uniform flow. (3.5 marks) (b) Determine the theoretical pressure distribution expression on the cylinder surface, Pc and plot or sketch a graph of...
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...
4. Air flows around a flat-bottomed airfoil shown in the figure. The air velocity at the edge of the boundary layer at the bottom is the free stream velocity, U, and at the top it is u(x). Determine the lift coefficient, CL , for this flow if u²(x) = U u = ulx) P, u(x) U pol
(3) As shown in the figure below, wind blows at a uniform, constant velocity of 60 mph over a six foot diameter, air- tight Quonset hut is located on a flat plain. Assume 2d, inviscid, irrotational flow and that the density of the air is 0.002 slug/ft? Voo a. Where on the surface of the hut should the vent A be located so that the pressure inside the hut is equal to P? b. Find the difference in static pressure...
QUESTION 3 (14 marks) Variation in drag cylinder is shown in Figure 2 (a) At point coefficient (CD) against Reynolds number (Re) for flow around a smooth a, point out whether drag is mainly contributed by pressure drag or friction (8 marks) drag, and explain the reason why (6 marks) (b) Explain the reason why there is a sudden drop in Co at point 400 200 100 40 20 10 60 N C, 6 Smoath cylinder 0.6 0.4 0.2 0.1...
3. Velocity profiles are measured at the upstream end (surface I) and at the downstream end (surface 2) of the control volume shown in figure below. Surfaces 3 and 4 are streamlines. If the flow is incompressible, two dimensional, and steady, what is the drag coefficient for the airfoil? The vertical dimension Hp = 0.025c. The pressure is Pao (a constant) over the entire surface of the control volume. Streamline (--v-(1-05000 )
2. Water flows over a flat surface at 8 m/s, as shown in figure. A pump draws off water through a narrow slit at a volume rate of 0.2 m2/s per meter length of the slit. Assume that the fluid is incompressible and inviscid and can be represented by the combination of a uniform flow and a sink. a) Based on method of superposition, propose a general expression for stream function ψ velocity potential ф, and velocity components of v,...
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