What is the significance of obtaining a maximum Reynolds number of 100,000 in a laboratory water system?
To achieve a maximum Reynolds number of 100,000 in a laboratory water system, it is important for studying flow in a smooth pipe. The Reynolds number is a dimensionless quantity that characterizes the flow regime in a pipe. By reaching the desired Reynolds number, researchers can study the flow behavior under turbulent flow conditions, which is typically characterized by Reynolds numbers above 4000. This allows for a more comprehensive understanding of fluid dynamics and flow patterns in the pipe system.
Calculating Minimum Height of Supply Tank
To calculate the minimum height of the supply tank above the pipe system discharge to reach the desired Reynolds number of 100,000, we need to determine the pressure head required to achieve this condition. The Reynolds number (Re) can be calculated using 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 pipe diameter
- μ is the dynamic viscosity of the fluid
In this case, we are given the maximum Reynolds number of 100,000 and the pipe diameter of 15.9 mm. By rearranging the formula, we can solve for the velocity (V):
V = (Re * μ) / (ρ * D)
Substitute the values into the equation:
V = (100,000 * μ) / (ρ * 15.9 mm)
Next, we need to calculate the pressure head required to achieve the desired flow rate. This can be done using the Darcy-Weisbach equation:
ΔP = f * (L / D) * (ρ * V^2) / 2
Where:
- ΔP is the pressure drop
- f is the Darcy friction factor
- L is the pipe length
- D is the pipe diameter
- ρ is the density of the fluid
- V is the velocity of the fluid
Since we want to calculate the minimum height of the supply tank, we need to consider the pressure head due to the difference in elevation between the supply tank and the pipe system discharge. This can be calculated using the hydrostatic pressure formula:
ΔP = ρ * g * Δh
Where:
- ρ is the density of the fluid
- g is the acceleration due to gravity
- Δh is the height difference between the supply tank and the pipe system discharge
By equating both pressure drop equations, we can determine the minimum height of the supply tank above the pipe system discharge required to achieve the desired Reynolds number of 100,000.