Week 2 - Sediment transport

Question 1

basic dimensions used to express variables in sediment transport

Answer 1

Mass, length, and time.

Question 2

What are the dimensions of density?

Answer 2

[ML^-3].

Question 3

What are the dimensions of force?

Answer 3

[MLT^-2].

Question 4

dimensions of velocity

Answer 4

[LT^-1].

Question 5

dimensions of acceleration

Answer 5

[LT^-2].

Question 6

dimensions of pressure?

Answer 6

[ML^-1T^-2].

Question 7

dimensions of shear stress?

Answer 7

[ML^-1T^-2].

Question 8

dimensions of viscosity?

Answer 8

[ML^-1T^-1]

Question 9

How is density defined?

Answer 9

Density (ρ) is the mass per unit volume, with dimensions [ML^-3].

Question 10

What are the common units of density?

Answer 10

kg/m³.

Question 11

How is specific weight (y) related to density?

Answer 11

Specific weight is y = ρg, with units N/m³.

Question 12

What is viscosity a measure of?

Answer 12

measure of the fluid’s resistance to deformation, or internal friction.

Question 13

What is shear stress?

Answer 13

the force per unit area (τ = F/A), with dimensions [ML^-1T^-2].

Question 14

What is the no-slip condition in fluid flow?

Answer 14

The velocity at the boundary should be zero, and adjacent particles must have the same velocity.

Question 15

What is the velocity gradient in fluid flow?

Answer 15

the velocity gradient is the change in velocity (du) over the change in elevation (dz), i.e., du/dz.

Question 16

What does Newton’s law of viscosity describe?

Answer 16

Relationship between shear stress and shear rate in a fluid subjected to mechanical stress.

Question 17

What is the equation relating shear stress and velocity gradient according to Newton’s law of viscosity?

Answer 17

τ = µ(du/dz), where µ is the dynamic viscosity.

Question 18

What is the dynamic (absolute) viscosity (µ)?

Answer 18

µ is the coefficient of proportionality in Newton’s law of viscosity, with dimensions [ML^-1T^-1].

Question 19

What is the kinematic viscosity?

Answer 19

Kinematic viscosity (ν) is the ratio of dynamic viscosity to density, with dimensions [L²T^-1].

Question 20

What is the relationship between dynamic viscosity and temperature?

Answer 20

Dynamic viscosity is temperature-dependent.

Question 21

What does the Reynolds number (Re) describe?

Answer 21

the ratio between inertial and viscous forces in a flow, helping to determine whether the flow is laminar or turbulent.

Question 22

What is the Reynolds number for flow in a pipe?

Answer 22

Re = (ρUL)/µ, where U is the flow velocity, L is the characteristic length (diameter), and µ is the dynamic viscosity, ρ is density

Question 23

What is the significance of a Reynolds number greater than 4000?

Answer 23

It indicates turbulent flow

Question 24

What are the flow states described by Reynolds’ number?

Answer 24

Laminar (<2000), turbulent (>4000), and transitional (between 2000-4000).

Question 25

What is the Froude number (Fr)?

Answer 25

The ratio of inertial to gravitational forces, used to describe flow states in open channels.

Question 26

What does a Froude number less than 1 indicate?

Answer 26

Sub-critical (tranquil) flow, where gravitational forces dominate

Question 27

What does a Froude number greater than 1 indicate?

Answer 27

Supercritical (shooting) flow, where inertial forces dominate.

Question 28

What is the shear velocity (u*)?

Answer 28

Shear velocity is defined as u* = √(τ₀/ρ), where τ₀ is the bed shear stress and ρ is fluid density.

Question 29

What is the boundary layer in fluid flow?

Answer 29

The boundary layer is the region near the bed where velocity changes from zero (at the boundary) to maximum (away from the boundary).

Question 30

What happens to bed shear stress in the laminar region?

Answer 30

As the boundary layer thickens, the bed shear stress (τ₀) decreases.

Question 31

What is the logarithmic velocity profile?

Answer 31

In turbulent flow, the velocity profile follows a logarithmic pattern in the boundary layer. Near the surface: The velocity increases rapidly from zero, but the rate of increase slows down. Farther from the surface: The velocity approaches a constant value as you get further away from the boundary.

Question 32

How can bed shear stress be estimated from velocity profiles?

Answer 32

Using the logarithmic velocity profile equations, bed shear stress can be estimated from measured velocity profiles.

Question 33

How is shear force on a granular bed calculated?

Answer 33

Shear stress (τ) is calculated as the force per unit area (τ = F/A), and it can be determined using either laminar or turbulent flow equations depending on the flow type.

Question 34

Shear stress laminar flow

Answer 34

calculated using 𝜏=𝜇(𝑑𝑢/𝑑z) where the velocity gradient is smooth and linear.

Question 35

Turbulent flow: Shear stress

Answer 35

using 𝜏=𝜌𝑢∗^2 where 𝑢* is the friction velocity, and the velocity profile follows a logarithmic pattern.