A liquid (? = 1.65 g/cm3) flows through a horizontal pipe of varying cross secti

Question

A liquid (? = 1.65 g/cm3) flows through a horizontal pipe of varying cross section as in the figure below. In the first section, the cross-sectional area is 10.0 cm2, the flow speed is 255 cm/s, and the pressure is 1.20 105 Pa. In the second section, the cross-sectional area is 3.50 cm2 (a) Calculate the smaller section's flow speed. __________m/s (b) Calculate the smaller section's pressure. ___________ Pa

Explanation / Answer

(a) Assume incompressible flow. Conservation of mass requires that the volumetric flow rate in both sections is the same. Since volumetric flow is average velocity times cross sectional area: v1 · A1 = v2 · A2 => v1= v2 · A2/ A1 = 2.95m/s · 10/3.5= 8.43m/s (b) Assume frictionless flow. Then the mechanical energy of the fluid stay constant and you can apply Bernoulli's equation p / ? + g·h + v²/2 = constant or p1 /? + g·h1 + v1²/2 = p2 /? + g·h2 + v2²/2 Because the pipes are horizontal h1= h2 p1 /? + v1²/2 = p2 /? + v2²/2 => p1= p2+ ( v2² - v1²) · ?/2 = 1.2·105Pa + ((2.95m/s)² - (8.43m/s)²) · 1650kg/m³ / 2 = 6.86·104Pa

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