no table and no diagram for this question

a)What speed would water have to drop below to deposit a 250μm diameter grain of sediment?......... answer to unit ms^-1

b)What speed would water have to drop below to deposit a 500μm diameter grain of sediment?...........answer to unit ms^-1

To answer these questions, we can use the concept of settling velocity, which is the speed at which a grain of sediment falls through a fluid (in this case, water) due to the force of gravity. The settling velocity depends on the size and shape of the sediment grain, as well as the properties of the fluid.

One popular equation that can be used to estimate the settling velocity of sediment is the Stokes Law:

V = (2/9) * (g * (ρp - ρf) * d^2) / μ

Where:
- V is the settling velocity (in meters per second, m/s)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- ρp is the density of the sediment particle (in kg/m^3)
- ρf is the density of the fluid (in kg/m^3, which is 1000 kg/m^3 for water)
- d is the diameter of the sediment particle (in meters)
- μ is the dynamic viscosity of the fluid (in kg/(m*s), which is approximately 0.001 kg/(m*s) for water)

Now let's solve each question:

a) For a 250μm diameter grain of sediment:
- Convert the diameter from micrometers (μm) to meters (m):
d = 250 * 10^-6 = 0.00025 m
- Plug the values into the Stokes Law equation:
V = (2/9) * (9.8 * (ρp - 1000) * (0.00025)^2) / 0.001
- Since we don't have the density of the sediment grain (ρp), we cannot determine the exact value. You can substitute an average value for ρp, depending on the type of sediment you are studying, and solve for V.

b) For a 500μm diameter grain of sediment:
- Convert the diameter from micrometers (μm) to meters (m):
d = 500 * 10^-6 = 0.0005 m
- Plug the values into the Stokes Law equation:
V = (2/9) * (9.8 * (ρp - 1000) * (0.0005)^2) / 0.001
- Again, we need the density of the sediment grain (ρp) to determine the exact value. Substitute an average value for ρp and solve for V.

Therefore, in order to find the speed at which the water needs to drop below to deposit a grain of sediment, you will need to know the density (ρp) of the sediment grain.