Worksheet: Laminar and Turbulent Flow of Viscous Fluids

In this worksheet, we will practice modeling the motion of viscous liquids that can have flow uniform laminar flow or non-uniform turbulent flow.

Q1:

Water flowing through a pipe has a dynamic viscosity of 8 . 9 × 1 0 Pa⋅s and a density of 1,000 kg/m3. The pipe has an internal diameter of 0.0055 m.

What average speed must the water flow stay below for the Reynolds number of the flow to stay below 2,300?

Above what average speed of water flow will the Reynolds number exceed 2,900?

Q2:

Water flowing through a pipe has a dynamic viscosity of 8 . 9 × 1 0 Pa⋅s and a density of 1,000 kg/m3. The pipe has an internal diameter of 0.025 m and the water flows at an average speed of 0.15 m/s. What is the Reynolds number for the flow?

Q3:

A viscous fluid flows in a pipe of constant cross-sectional area perpendicular to the flow direction. The diagram shows a cross section of the pipe parallel to the flow direction. The fluid moves in horizontal layers in laminar flow at speeds 𝑣 to 𝑣 . Which of the following correctly describes the relationship between the speeds of the layers?

  • A 𝑣 = 𝑣 = 𝑣 = 𝑣 = 𝑣
  • B 𝑣 > 𝑣 , 𝑣 = 𝑣 , 𝑣 > 𝑣 , 𝑣 = 𝑣
  • C 𝑣 = 𝑣 , 𝑣 > 𝑣 , 𝑣 = 𝑣 , 𝑣 > 𝑣
  • D 𝑣 > 𝑣 > 𝑣 > 𝑣 > 𝑣
  • E 𝑣 < 𝑣 < 𝑣 < 𝑣 < 𝑣

Q4:

The diagrams shown represent the boundaries of the layers of a viscous liquid, which move at different speeds when the liquid flows through a container. Which of the diagrams correctly represents the boundaries of the layers for the liquid flowing through a container in which the top of the container is moved relative to the base of the container?

  • A
  • B

Q5:

A volume of a viscous fluid is contained between two parallel horizontal plates, as shown in the diagram. The plate above the volume of fluid moves horizontally at a speed 𝑣 . Horizontal layers of the fluid move in laminar flow at speeds 𝑣 to 𝑣 . Which of the following correctly describes the relationship between the speeds of the layers?

  • A 𝑣 > 𝑣 > 𝑣 > 𝑣 > 𝑣
  • B 𝑣 = 𝑣 = 𝑣 = 𝑣 = 𝑣
  • C 𝑣 > 𝑣 , 𝑣 = 𝑣 , 𝑣 = 𝑣 , 𝑣 > 𝑣
  • D 𝑣 < 𝑣 , 𝑣 = 𝑣 , 𝑣 = 𝑣 , 𝑣 < 𝑣
  • E 𝑣 > 𝑣 > 𝑣 > 𝑣 > 𝑣

Q6:

A volume of a nonviscous fluid is contained between two parallel horizontal plates, as shown in the diagram. The plate above the volume of the fluid moves horizontally at a speed 𝑣 . Horizontal layers of the fluid move at speeds 𝑣 to 𝑣 . Which of the following correctly describes the relationship between the speeds of the layers?

  • A 𝑣 > 𝑣 > 𝑣 > 𝑣 > 𝑣
  • B 𝑣 = 𝑣 = 𝑣 = 𝑣 = 𝑣
  • C 𝑣 > 𝑣 , 𝑣 = 𝑣 , 𝑣 = 𝑣 , 𝑣 > 𝑣
  • D 𝑣 < 𝑣 , 𝑣 = 𝑣 , 𝑣 = 𝑣 , 𝑣 < 𝑣
  • E 𝑣 > 𝑣 > 𝑣 > 𝑣 > 𝑣

Q7:

The diagrams shown represent the boundaries of the layers of a viscous liquid that move at different speeds when the liquid flows through a pipe. Which of the diagrams correctly represents the boundaries of the layers for the liquid?

  • A
  • B

Q8:

A thin plate of mass 2.5 g is pushed by a constant force 𝐹 = 0 . 5 0 m N , moving at a constant 1.20 cm/s over the surface of a viscous liquid that is 2.5 mm deep, as shown in the diagram. The speeds of the layers of the liquid between the plate and the lowest layer of the liquid are shown in the diagram. The liquid in contact with the top and bottom plates move at the same speed as the plates move. What is the dynamic viscosity of the liquid?

  • A 1 . 7 × 1 0 Pa⋅s
  • B 9 . 4 × 1 0 Pa⋅s
  • C 8 . 5 × 1 0 Pa⋅s
  • D 5 . 5 × 1 0 Pa⋅s
  • E 3 . 0 × 1 0 Pa⋅s

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