Question

Question 1 1 pts Water at 15°C is flowing at 50 cm3/s in a pipe. The pipe diameter is 10 cm and the length is 10 m. Determine Reynold's number (Re) and decide whether the flow is laminar or turbulent

Answer 1

the Reynolds number is 4397, which is greater than 4000. Therefore, the flow of water in the pipe is likely to be turbulent.

Step-by-step explanation:

To determine the Reynolds number (Re) and decide whether the flow is laminar or turbulent, we can use the following formula:

Re = (ρ * v * d) / μ

Where:

• Re is the Reynolds number
• ρ is the density of the fluid
• v is the velocity of the fluid
• d is the diameter of the pipe
• μ is the dynamic viscosity of the fluid

Given:

• Fluid: Water at 15°C
• Flow rate: 50 cm^3/s
• Pipe diameter: 10 cm
• Pipe length: 10 m

First, we need to convert the flow rate from cm^3/s to m^3/s:

Flow rate = 50 cm^3/s = 50 * 10^(-6) m^3/s

Next, we need to determine the values of density (ρ) and dynamic viscosity (μ) for water at 15°C. At this temperature, the density of water is approximately 999 kg/m^3, and the dynamic viscosity is approximately 1.139 * 10^(-3) Pa·s.

Now we can calculate the Reynolds number (Re):

Re = (ρ * v * d) / μ

Re = (999 kg/m^3 * 50 * 10^(-6) m^3/s * 10 cm) / (1.139 * 10^(-3) Pa·s)

After performing the calculations, the Reynolds number (Re) is approximately 4397.

To determine whether the flow is laminar or turbulent, we can use the Reynolds number as a criterion. In general, flows with Re < 2000 are considered laminar, while flows with Re > 4000 are considered turbulent. If the Reynolds number falls between 2000 and 4000, the flow is in a transitional regime.

In this case, the Reynolds number is 4397, which is greater than 4000. Therefore, the flow of water in the pipe is likely to be turbulent.

Answer 2

To determine the Reynolds number (Re) and decide whether the flow is laminar or turbulent, we can use the formula:

Re = (ρ * v * D) / μ

Where:

Re is the Reynolds number

ρ is the density of the fluid

v is the velocity of the fluid

D is the characteristic length (pipe diameter)

μ is the dynamic viscosity of the fluid

Given:

Density of water (ρ) = 1000 kg/m^3

Velocity of water (v) = 50 cm^3/s = 0.05 m^3/s

Pipe diameter (D) = 10 cm = 0.1 m

Dynamic viscosity of water (μ) = 0.001 kg/(m·s)

Substituting the given values into the formula:

Re = (1000 kg/m^3 * 0.05 m^3/s * 0.1 m) / (0.001 kg/(m·s))

Re = 5000 / 0.001

Re = 5,000,000

The Reynolds number (Re) is 5,000,000.

To determine whether the flow is laminar or turbulent, we can use the following guidelines:

- For Re < 2000, the flow is laminar.

- For 2000 < Re < 4000, the flow is transitional.

- For Re > 4000, the flow is turbulent.

In this case, since Re = 5,000,000, which is significantly greater than 4000, the flow is considered turbulent.

Step-by-step explanation: