Solve 0.3m Diameter Cork Ball Drag Question in River

[kieranl]

Homework Statement

A 0.3m diameter cork ball (density 210kg/m^3) is tied to an object on the bottom of a river as is shown in fig B3. The weight of the cable and the drag on it can be neglected. Assume the water viscosity u is 1.12x10^-3 Ns/M^2 and the water density p is 1000kg/m^3, and the acceleration of gravity is 10ms^-2. Estimate the speed of the river current.

Homework Equations

Cd=(2Fd)/(pV^2A)

The Attempt at a Solution

I can calculate the tension of the cable and then find the Fd force but don't know how to apply it to find the velocity because I don't know what Cd is? There is an equation where Cd=24.0/Re but i don't see how i can use that either. please help?

 

[Jhero]

Dear forum post author,

Thank you for your question. In this scenario, Cd refers to the drag coefficient of the object in the water. This value depends on the shape and size of the object and can be found in a table or calculated using experimental data. Since the object in this case is a cork ball, we can assume a spherical shape and use the standard drag coefficient for a sphere, which is approximately 0.47.

To find the velocity of the river current, we can use the equation you mentioned: Cd=(2Fd)/(pV^2A). Rearranging this equation, we get V = √(2Fd)/(pCdA). We already know the values for p, Fd, and A (water density, drag force, and cross-sectional area of the cork ball), so we just need to find the value of Cd.

To calculate Cd, we can use the formula Cd=24.0/Re, where Re is the Reynolds number. This is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid. In this case, the Reynolds number can be calculated as Re = (density x velocity x diameter)/viscosity. Plugging in the given values, we get Re = (1000 kg/m^3 x V x 0.3m)/(1.12x10^-3 Ns/m^2) = 267857V.

Now, we can substitute this value of Re into the equation for Cd and solve for V. We get Cd = 24.0/267857V, which simplifies to Cd = 8.95x10^-5/V. Substituting this into our original equation, we get V = √(2Fd)/(pCdA) = √(2 x Fd)/(p x 8.95x10^-5 x A). Plugging in the known values, we get V = √(2 x 0)/(1000 x 8.95x10^-5 x π(0.15)^2) = 0 m/s.

This means that the velocity of the river current is approximately 0 m/s, since the drag force on the cork ball is equal to the weight of the ball and there is no net force acting on it. I hope this helps to answer your question. Please let me know if you have any further questions.