A fluid is flowing with an average speed of 1.50 m/s through a tube that has a radius of 2.00 mm and is 18 cm long. The drop in pressure is 967 Pa. What is the viscosity of the fluid? A) 0.00179 Ns/m² B) 0.00562 Ns/m² C) 0.0278 Ns/m² D) 0.0134 Ns/m² E) 0.00335 Ns/m²

Question

Quizplus · Accepted Answer

Explanation:The pressure drop in a fluid flowing through a tube is given by the Hagen-Poiseuille equation:$$\Delta P = \frac{8\mu L Q}{\pi r^4}$$where:* $\Delta P$ is the pressure drop (967 Pa)* $\mu$ is the viscosity of the fluid (unknown)* $L$ is the length of the tube (18 cm = 0.18 m)* $Q$ is the volumetric flow rate (unknown)* $r$ is the radius of the tube (2.00 mm = 0.002 m)The volumetric flow rate can be calculated from the average speed and the cross-sectional area of the tube:$$Q = Av = \pi r^2 v$$where:* $A$ is the cross-sectional area of the tube ($\pi r^2$)* $v$ is the average speed of the fluid (1.50 m/s)Substituting the expressions for $Q$ and $\Delta P$ into the Hagen-Poiseuille equation, we get:$$\frac{8\mu L \pi r^2 v}{\pi r^4} = 967 ext{ Pa}$$Solving for $\mu$, we get:$$\mu = \frac{967 ext{ Pa} imes 0.002^4 ext{ m}^4}{8 imes 0.18 ext{ m} imes \pi imes 1.50 ext{ m/s}} = 0.00179 ext{ Ns/m}^2$$Therefore, the viscosity of the fluid is 0.00179 Ns/m².

A Fluid Is Flowing with an Average Speed of 1