water 20 degrees celsius flows through a 25 mm diameter pipe at a rate of 50 liters per minute.
is this laminar or turbulant flow or both?
Calculate the dimensionless Reynolds number,
Re = (rho)*D*V/(viscosity)
The flow is
* laminar when Re < 2300
* transitional when 2300 < Re < 4000
* turbulent when Re > 4000
The viscosity of water at 20 C is
mu = 1.002*10^-3 N*s/m^2 or kg/m*s
The pipe cross sectional area is A = 4.904*10^-4 m^2
The velocity at the flow rate mentioned is
V = (50*10^-3 m^3/s)/4.904*10^-2 m^2
= 102 m/s
The water density is 1000 kg/m^w3
Reynolds number is
(10^3)*2.5*10^-2*102/1.002*10^-3
2.5*10^6
Not even close. It is turbulent flow
To determine if the flow of water through the pipe is laminar or turbulent, we can use the Reynolds number (Re). The Reynolds number describes the flow regime and is calculated using the following formula:
Re = (ρ * V * D) / μ
where:
- ρ is the density of the fluid (in kg/m^3)
- V is the velocity of the fluid (in m/s)
- D is the diameter of the pipe (in m)
- μ is the dynamic viscosity of the fluid (in kg/(m*s))
In this case, we are given:
- The density of water at 20 degrees Celsius is approximately 998 kg/m^3
- The velocity of water is 50 liters per minute, which needs to be converted to m/s
- The diameter of the pipe is 25 mm, which needs to be converted to meters
- The dynamic viscosity of water at 20 degrees Celsius is approximately 0.001 kg/(m*s)
First, let's convert the given values to the required units:
- 50 liters per minute is equivalent to (50/60) m^3/s
- The diameter of the pipe in mm is 25 mm, which is equivalent to 0.025 m
Now, we can substitute the values into the Reynolds number equation:
Re = (998 * (50/60) * 0.025) / 0.001
After calculating this expression, we find that the Reynolds number is approximately 83.23.
In fluid dynamics, flow can be classified as follows:
- Laminar flow: Re < 2000
- Turbulent flow: Re > 4000
- Transitional flow: 2000 < Re < 4000
Since the Reynolds number in this case is approximately 83.23, it falls within the range for laminar flow. Therefore, the flow of water through the 25 mm diameter pipe at a rate of 50 liters per minute is laminar.