Glycerin,with a viscosity of 1.5 N ∙ s/m²,is flowing with an average speed of 1.2 m/s through a tube that has a radius of 5.0 mm and is 25 cm long.What is the drop in pressure over the length of this pipe? A)140 kPa B)46 kPa C)72 kPa D)76 kPa E)130 kPa

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Quizplus · Accepted Answer

The drop in pressure is given by the Hagen-Poiseuille equation:$$\Delta P = \frac{8\mu L Q}{\pi r^4}$$where:* $\Delta P$ is the drop in pressure (Pa)* $\mu$ is the viscosity (N ∙ s/m²)* $L$ is the length of the pipe (m)* $Q$ is the flow rate (m³/s)* $r$ is the radius of the pipe (m)We can calculate the flow rate from the average speed and the cross-sectional area of the pipe:$$Q = Av = \pi r^2 v$$where:* $A$ is the cross-sectional area of the pipe (m²)* $v$ is the average speed (m/s)Substituting the given values into the Hagen-Poiseuille equation, we get:$$\Delta P = \frac{8\mu L Q}{\pi r^4} = \frac{8(1.5 ext{ N} \cdot ext{s/m}^2)(0.25 ext{ m})(\pi (5.0 imes 10^{-3} ext{ m})^2 (1.2 ext{ m/s}))}{\pi (5.0 imes 10^{-3} ext{ m})^4} = 140 ext{ kPa}$$Therefore, the drop in pressure over the length of the pipe is 140 kPa.

Glycerin,with a Viscosity of 1