Glycerine of density 1.25*10³ kg/m³ flows through a tapering (conical) pipe whose end radii are 0.1 m and 0.04 m. The pressure difference across the pipe is 10 N/m². Calculate the volume rate of flow of the glycerine.

6.4*10⁻⁴ m³/s
1.0*10⁻⁴ m³/s
2.0*10⁻⁴ m³/s
3.0*10⁻⁴ m³/s

Correct answer: 6.4*10⁻⁴ m³/s

Solution

By continuity A1*v1 = A2*v2 = Q. Bernoulli (horizontal): P1 - P2 = (1/2)*rho*(v2² - v1²). With r1 = 0.1, r2 = 0.04, A1/A2 = (0.1/0.04)² = 6.25. The narrower end has the higher speed. Solving gives Q approximately 6.4*10⁻⁴ m³/s, the standard textbook result.

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