 When considering flow through a circular pipe, we use a Reynolds number with respect to diameter of 2,300 as the critical Reynolds number. For flow through a 5 centimeter diameter pipe, at what velocity will transition occur at 20 degrees Celsius for airflow and water flow in meters per second? We'll start with air. We're using a Reynolds number with respect to diameter of 2,300 because that's our critical Reynolds number. And we are solving for velocity. We know that Reynolds number is velocity times density times whatever we're using as a size parameter, in this case diameter, divided by dynamic viscosity. Or for convenience, we can introduce a simplified normalized viscosity called kinematic viscosity, which is dynamic viscosity divided by density. In that case, our Reynolds number would just be velocity times diameter divided by kinematic viscosity. When we're talking about the properties of air, we need to jump into our appendices and the relevant table is going to be table A2. A2 contains properties including density, dynamic viscosity, and kinematic viscosity for air at a variety of temperatures. Using 20 degrees Celsius, we could look up the density and the dynamic viscosity separately. Or because of the simplification, we can get away with looking up just a single parameter, kinematic viscosity, at what point we only have to plug in a single number. So in our equation, we're going to use a kinematic viscosity for air at 20 degrees Celsius, and that number is 1.5 times 10 to the negative fifth meter squared per second. If we're solving for velocity, that means we'll take 2,300 because that's our critical Reynolds number, which is what we are trying to calculate a velocity for, multiplied by kinematic viscosity, divided by diameter. Then we're taking 2,300 multiplied by 1.5 times 10 to the negative fifth meter squared per second, and we are dividing by the diameter of our pipe, the diameter is 5 centimeters, and because we want a velocity in meters per second, we're going to have to convert centimeters to meters, then centimeters cancel centimeters, the meters cancel one of the meters in the square, leaving us with meters per second. If I pop up my calculator, surely it will cooperate. I can take 2,300 multiplied by 1.5 times 10 to the negative fifth times 100 divided by 5, and I get a velocity of 0.69 meters per second. So for air flowing through a 5 centimeter diameter pipe, anything slower than 0.69 meters per second on average, we will call laminar flow. Any velocity higher than 0.69 meters per second, we will call turbulent flow. We can repeat the process for water. The only thing that we would have to change is the kinematic viscosity for water. For water properties, we're going to use table A1. We still have a temperature of 20 degrees, and again we can look up the density and the dynamic viscosity and plug them both in. Or for convenience, we can use a single parameter, the kinematic viscosity, and plug in a single number. So the kinematic viscosity of water at 20 degrees Celsius is 1.005 times 10 to the negative sixth meters squared per second. Then when we take 2,300 times our kinematic viscosity divided by diameter, we will end up with a velocity again. And just like before, we have to convert centimeters to meters in order to yield an answer in meters per second. And just like before, I can try to get my calculator to cooperate. We get a velocity of 0.04623. So when considering a flow of water through a 5 centimeter diameter pipe, any average velocity less than 0.04623 meters per second we will call laminar, any velocity higher than 0.04623 we will call turbulent. We can conclude from our calculation here that for a given velocity through a given pipe, water will be much more turbulent than air.