An incompressible fluid is flowing through a pipe with a constriction. The pipe
ID: 2115847 • Letter: A
Question
An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees. The narrow section is 10.0 m from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is 4.00 m/s. The diameter of the wide section is 12.00 cm and the diameter of the narrow section is 9.00 cm. The pressure of the fluid in the wide section is 250 kPa. What is the pressure in the narrow section of the pipe? (density of the fluid is 1,000 kg/m3)
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Explanation / Answer
An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 30.0 degrees. The narrow section is 10.0 m from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is 4.00 m/s. The diameter of the wide section is 12.00 cm and the diameter of the narrow section is 9.00 cm. The pressure of the fluid in the wide section is 250 kPa. What is the pressure in the narrow section of the pipe? (density of the fluid is 1,000 kg/m3) The velocity is inversely proportional to the cross-sectional area of the pipe. v1 * A1 = v2 * A2 v1 * (p * 4.5^2) = 4.00 * p * 6^2 v1 = (4.00 * p * 6^2) ÷ (p * 4.5^2) = 7.11 m/s This is the velocity in the narrow section. The narrow section is 10.0 m from the wide section and the narrow section is lower than the wide section. So, the difference in height = 10.0 * sin 30° The narrow section is 5 m is lower than the wide section. Now it’s Bernoulli time! P1 + ½ * 1000 * v1^2 + density * g * h1 = P2 + ½ * density * v2^2 + density * g * h2 v1 = 7.11 m/s, v2 = 4 m/s h1 = 0 m, h2 = 5 m P2 = 250 P1 + ½ * 1000 * 7.11^2 + 1000 * 9.8 * 0 = 250 + ½ * 1000 * 4^2 + 1000 * 9.8 * 8
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