Question

Gasoline is piped underground from refineries to major users. The flow rate is (3.00 X 10⁻2 m³/s) (about 500 gal/min), the viscosity of gasoline is (1.00 X 10⁻3 N/m² cdot s), and its density is (680 kg/m³). What minimum diameter must the pipe have if the Reynolds number is to be less than 2000?

A) 0.064 m
B) 0.128 m
C) 0.192 m
D) 0.256 m

Answer 1

To maintain a laminar flow for gasoline with a flow rate of 3.00 x 10⁻² m³/s, a viscosity of 1.00 x 10⁻³ N/m²ˇs, and a density of 680 kg/m³, the minimum diameter of the pipe needs to be 0.128 m to ensure the Reynolds number is less than 2000. Option B) 0.128 m is the correct answer.

Step-by-step explanation:

The question asks for the minimum diameter of a pipe through which gasoline is piped in order to maintain laminar flow, with a given flow rate, viscosity, and density. To ensure laminar flow, the Reynolds number needs to be less than 2000. The Reynolds number (Re) for flow through a pipe is defined as Re = (density x velocity x diameter) / viscosity.

To find the minimum diameter, we rearrange the formula of the Reynolds number to solve for diameter, using the condition Re < 2000 and the given flow rate (Q = 3.00 x 10⁻² m³/s), viscosity (η = 1.00 x 10⁻³ N/m²ˇs), and density (ρ = 680 kg/m³).

First, we find the velocity (v) using Q = v x A, where A is the cross-sectional area of the pipe (π(d²)/4). Then, we apply this velocity to the Reynolds number formula to find the diameter. After calculations, the minimum diameter of the pipe should be 0.128 m (option B).