Final answer:
In order to maintain the movement of a 1.0-cm particle through a stream, we need a stream velocity that is greater than or equal to the settling velocity of the particle. Specific values will be required to provide a numerical answer.
Step-by-step explanation:
In order to maintain the movement of a 1.0-cm particle through a stream, you need a stream velocity that is greater than or equal to the settling velocity of the particle.
To calculate the settling velocity of the particle, you can use Stokes' law.
Stokes' law states that the settling velocity (Vs) of a particle in a fluid is given by the equation: Vs = (2/9) * (r^2) * (g) * (p - pf) / (n)
where: - r is the radius of the particle (0.5 cm in this case, as the particle has a diameter of 1.0 cm)
Assuming the particle is spherical, we can calculate its volume using the formula for the volume of a sphere: V = (4/3) * π * (r^3)
To calculate the density of the particle, we need to know its mass.
Let's assume the particle is made of a material with a known density, such as plastic with a density of 1.0 g/cm^3.
We can then calculate the mass (m) of the particle using its volume (V) and the density of the material: m = V * p
Now that we have the mass of the particle, we can substitute it into the equation for the settling velocity: Vs = (2/9) * (r^2) * (g) * (p - pf) / (n)
Note that the units of the variables in the equation should be consistent.
For example, if the radius is given in centimeters, the density should also be in grams per cubic centimeter, and the viscosity in poise or centipoise.