# Resultant velocity of submerged cylinder

• peasant
In summary, to calculate the resultant velocity of a cylinder immersed in water with a current, you will need to consider the forces acting on the cylinder, including the force of the current, the weight of the cylinder, and the frictional force. Using Newton's second law and the kinematic equations, you can calculate the acceleration and velocity of the cylinder. The frictional force can be calculated using the equation for drag force. Finally, you can use vector addition to calculate the resultant velocity of the cylinder.
peasant
Hi all, this is not a homework question so it does not have a given answer and the question may be vague. It is something I need to know for my project, hope you guys can just give a few tips to point me in the right direction. Thanks.

## Homework Statement

A cylinder of radius r metres, length L and mass m kg is immersed d metres in the sea. It is at static equilibrium along the z-axis. Friction is not negligible. If there is an underwater current of velocity v metres/sec, what is the resultant velocity of the cylinder?
When the cylinder is moving at velocity v_c, I could add the velocity vectors v and v_c to get the resultant velocity, but I also wish to factor in the mass of the cylinder. How should I do that?

none

## The Attempt at a Solution

When the current hits the cylinder, the cylinder accelerates and frictional force increases. The cylinder then reaches terminal velocity. But what I don't get is how to calculate the force of the current on the cylinder and the frictional force .

Hi there,

Your project sounds interesting! To calculate the resultant velocity of the cylinder, you will need to consider the forces acting on the cylinder in the water. These include the force of the current, the weight of the cylinder, and the frictional force.

To start, you can use Newton's second law (F=ma) to calculate the acceleration of the cylinder. The mass of the cylinder will factor into this equation, so make sure to include it. You can then use the kinematic equations to calculate the velocity of the cylinder as it accelerates.

Next, you will need to consider the frictional force acting on the cylinder. This will depend on the surface area of the cylinder, the properties of the water, and the velocity of the cylinder. You can use the equation for drag force (F= 1/2 * p * v^2 * Cd * A) to calculate the frictional force, where p is the density of the water, v is the velocity of the cylinder, Cd is the drag coefficient, and A is the surface area of the cylinder.

Finally, you can use vector addition to calculate the resultant velocity of the cylinder. This will involve adding the velocity of the cylinder due to the current to the velocity of the cylinder due to acceleration and taking into account the direction of the forces.

I hope this helps point you in the right direction. Good luck with your project!

## 1. What is the definition of resultant velocity of submerged cylinder?

The resultant velocity of a submerged cylinder is the final velocity or speed at which the cylinder moves after being completely submerged in a fluid or liquid.

## 2. How is resultant velocity of submerged cylinder calculated?

The resultant velocity of submerged cylinder can be calculated using the equation: V = √(2gh), where V is the resultant velocity, g is the acceleration due to gravity, and h is the height of the fluid above the cylinder.

## 3. What factors affect the resultant velocity of submerged cylinder?

The resultant velocity of submerged cylinder is affected by various factors such as the density of the fluid, the shape and size of the cylinder, and the angle of immersion.

## 4. Can resultant velocity of submerged cylinder be negative?

Yes, resultant velocity of submerged cylinder can be negative if the cylinder is moving downwards against the direction of the fluid flow or if the cylinder is experiencing resistance from the fluid.

## 5. How is the resultant velocity of submerged cylinder different from the velocity of the fluid?

The resultant velocity of submerged cylinder is the final velocity of the cylinder after being submerged, whereas the velocity of the fluid is the speed at which the fluid is flowing. These velocities can be different depending on the factors affecting the cylinder's motion in the fluid.

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