20°C water flows through a 2.0-m-long, 6.0-mm-diameter pipe. What is the maximum flow rate in L/min for which the flow is laminar?
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Identify the properties of the fluid and the pipe. Here, the fluid is water at 20°C, the length of the pipe (L) is 2.0 m, and the diameter (D) of the pipe is 6.0 mm.
Convert the diameter from millimeters to meters for consistency in units. Since 1 mm = 0.001 m, a 6.0 mm diameter equals 0.006 m.
Use the Reynolds number formula for determining the flow regime. The Reynolds number (Re) is given by Re = \( \frac{\rho v D}{\mu} \), where \( \rho \) is the density of the fluid, \( v \) is the flow velocity, \( D \) is the diameter of the pipe, and \( \mu \) is the dynamic viscosity of the fluid.
Find the values for the density and dynamic viscosity of water at 20°C. Typically, \( \rho \approx 998 \, \text{kg/m}^3 \) and \( \mu \approx 0.001 \, \text{Pa} \cdot \text{s} \) for water at this temperature.
Calculate the maximum flow velocity for laminar flow by ensuring the Reynolds number is less than 2000. Solve for \( v \) in the Reynolds number equation using the critical value of 2000, and then calculate the flow rate (Q) using the formula Q = \( v \times \text{Area} \), where Area = \( \pi \times \left(\frac{D}{2}\right)^2 \). Convert the flow rate from cubic meters per second to liters per minute for the final answer.