Impure water at 20^∘ C enters the retention tank and rises...

Impure water at $20^{\circ} \mathrm{C}$ enters the retention tank and rises to a level of $2 \mathrm{~m}$ when it stops flowing in. Determine the shortest time needed for all sediment particles having a diameter of $0.05 \mathrm{~mm}$ or greater to settle to the bottom. Assume the density of the particles is $\rho=1.6 \mathrm{Mg} / \mathrm{m}^{3}$ or greater.

Key Concepts

Stokes' Law

Stokes' law describes the drag force experienced by small spherical particles moving in a viscous fluid under laminar flow conditions. This law allows for the calculation of the terminal settling velocity by relating the size and density of the particle, the viscosity of the fluid, and the gravitational force, which is critical for understanding sedimentation in fluids.

Terminal Settling Velocity

Terminal settling velocity is the steady speed achieved by a particle as it falls through a fluid when the gravitational force is balanced by the drag and buoyancy forces. Calculating this velocity is essential for determining how long it takes for particles to settle, a fundamental aspect in designing sedimentation processes.

Sedimentation Process

Sedimentation is the process by which suspended particles gradually settle out of a fluid due to the force of gravity. This process is widely used in environmental engineering and water treatment to remove impurities from water by allowing particles to settle in a designated area or tank.

Retention Tank Dynamics

Retention tank dynamics involve the design and operational considerations of tanks where sedimentation occurs. Key parameters include the depth or settling distance, inflow velocities, and retention time, all of which ensure that particles have sufficient time to settle out of the fluid, thereby improving the efficiency of water treatment systems.

Particle Size and Density Effects

The settling rate of particles in a fluid is significantly influenced by their size and density. Larger and denser particles have higher gravitational forces acting on them, resulting in faster settling, while smaller particles or those with densities closer to the fluid density settle more slowly. Understanding these effects is crucial for effective sedimentation design and analysis.

Transcript

00:01 Consider this diagram.

00:02 We're told that in pure water, 20 degrees, enters the retention tank, rising to a level of two meters when it stops flowing in.

00:09 And we're asked to find the shortest amount of time possible or required for all of the sediment.

00:17 Volume of the spheres, given as four -thirds pi are cubed.

00:22 Okay.

00:26 And we're told that the density asked to determine the shortest time needed for all sediment particles with a diameter of 0 .05 millimeters or gross.

00:34 To settle to the bottom.

00:36 We're given the density of the particles, and we're told how to calculate the volume of a sphere.

00:44 So our kinematic viscosity, let's figure this out, our density of air will be equal to 9, 9, 3, or 8.

00:59 0 .3 kilograms per meter cubed at 20 degrees, and our kinematic viscosity will be equal to 10 to the minus 6.

01:14 Let's convert density.

01:21 So we're given our density of 1 .6.

01:32 That'll be 1 .6 times 10 to the third kilograms per meter cubed.

01:43 And let's think of our sum of forces.

01:53 So we'll have fb to buoyancy and our drag and our weight.

02:07 Okay.

02:07 Our mass of our particle will be our density times our volume, and that will equal 1 ,600 kilograms per meter cubed times 4 thirds pi are cubed.

02:40 So that'll be 1 ,600.

02:42 I'll leave my units off this part, times 4 thirds pi, and then this will be 0 .025 meters.

02:53 Over 1 ,000 cubed.

02:58 So my mass of my particle will equal 1 .04719 times 10 to the minus 10th kilograms.

03:08 Underline that for when i need it...

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