1. Liquid Rotation in a Cylindrıcal Container You are to simulate a rotational liquid in a partially filled cylindrical container. Assuming the liquid rotates as a rigid body with the container, it experiences radially outward forces, or also known as the centrifugal forces. Thus, the fluid is seemed to be pushed towards the container's wall and the free surface of the liquid becomes concave as shown in Fig. 1. When the liquid is spinning too fast, the liquid may spill from the edges of the container. The liquid free surface profile/height, za at different radius from the rotation axis r, in Fig. 2 is represented by 2 = ha - (1) where ho is the original liquid height, w is the angular velocity of the liquid. g is the gravitational field strength, given at 9.812 m/s² and Ris the radius of the container. The liquid will start to spill when the height at the edge is higher than the cylinder's wall. THE SITUATION: A vertical cylindrical container with diameter of 4 mand height of 2.5 mis filled with water until the water height is 4/5 of the container's. The cylinder is then rotated slowly until the water within spins at the same speed. Write a MATLAB program to simulate the above situation to visualise and analyse the water profile. Your program should be able to: 1. Advise the user on the range of plausible obefore the water starts to spill (use Equation (1)) and request the user input for desired angular velocity, @. 2. Plot the cross-sectional water profile along the diameter of the cylinder. • Set up sufficient discrete points along the cross-sectional domain, x= [0,4]. • Compute the water height profile based on Equation (1) and plot it on the domain. Hints: r = |x- xe| where x: is at the centre of the cylinder. • Plot the still water profile before the rotation (z = ho) on the same axis. • Set up suitable legend to differentiate rotating water profile and still water profile. 3. Mark and label the minimum point of the rotating water profile as "Minimum Point". 4. Output the water height difference between the maximum and the minimum points.

1. Liquid Rotation in a Cylindrıcal Container You are to simulate a rotational liquid in a partially filled cylindrical container. Assuming the liquid rotates as a rigid body with the container, it experiences radially outward forces, or also known as the centrifugal forces. Thus, the fluid is seemed to be pushed towards the container's wall and the free surface of the liquid becomes concave as shown in Fig. 1. When the liquid is spinning too fast, the liquid may spill from the edges of the container. The liquid free surface profile/height, za at different radius from the rotation axis r, in Fig. 2 is represented by 2 = ha - (1) where ho is the original liquid height, w is the angular velocity of the liquid. g is the gravitational field strength, given at 9.812 m/s² and Ris the radius of the container. The liquid will start to spill when the height at the edge is higher than the cylinder's wall. THE SITUATION: A vertical cylindrical container with diameter of 4 mand height of 2.5 mis filled with water until the water height is 4/5 of the container's. The cylinder is then rotated slowly until the water within spins at the same speed. Write a MATLAB program to simulate the above situation to visualise and analyse the water profile. Your program should be able to: 1. Advise the user on the range of plausible obefore the water starts to spill (use Equation (1)) and request the user input for desired angular velocity, @. 2. Plot the cross-sectional water profile along the diameter of the cylinder. • Set up sufficient discrete points along the cross-sectional domain, x= [0,4]. • Compute the water height profile based on Equation (1) and plot it on the domain. Hints: r = |x- xe| where x: is at the centre of the cylinder. • Plot the still water profile before the rotation (z = ho) on the same axis. • Set up suitable legend to differentiate rotating water profile and still water profile. 3. Mark and label the minimum point of the rotating water profile as "Minimum Point". 4. Output the water height difference between the maximum and the minimum points.

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Figure 1: Schematie diagram of a liquid in rotating cylindrical container.
ho
Figure 2: Cross-sectional view of the rigid-body motion of a liquid in rotating eylindrical con-
tainer.

Transcribed Image Text:1. Liquid Rotation in a Cylindrical Container You are to simulate a rotational liquid in a partially filled cylindrical container. Assuming the liquid rotates as a rigid body with the container, it experiences radially outward forces, or also known as the centrifugal forces. Thus, the fluid is seemed to be pushed towards the container's wall and the free surface of the liquid becomes concave as shown in Fig. 1. When the liquid is spinning too fast, the liquid may spill from the edges of the container. The liquid free surface profile/height, z at different radius from the rotation axis r, in Fig. 2 is represented by 2 = ha - tR? - 27) where ho is the original liquid height, @ is the angular velocity of the liquid. g is the gravitational field strength, given at 9.812 m/s and Ris the radius of the container. The liquid will start to spill when the height at the edge is higher than the cylinder's wall. (1) THE SITUATION: A vertical cylindrical container with diameter of 4 mand height of 2.5 mis filled with water until the water height is 4/5 of the container's. The cylinder is then rotated slowly until the water within spins at the same speed. Write a MATLAB program to simulate the above situation to visualise and analyse the water profile. Your program should be able to: 1. Advise the user on the range of plausible obefore the water starts to spill (use Equation (1)) and request the user input for desired angular velocity, a. 2. Plot the cross-sectional water profile along the diameter of the cylinder. • Set up sufficient discrete points along the cross-sectional domain, x = [0,4). • Compute the water height profile based on Equation (1) and plot it on the domain. Hints: r= |x- xe| where xe is at the centre of the cylinder. • Plot the still water profile before the rotation (z = ho) on the same axis. • Set up suitable legend to differentiate rotating water profile and still water profile. 3. Mark and label the minimum point of the rotating water profile as "Minimum Point". 4. Output the water height difference between the maximum and the minimum points.

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