An incompressible fluid is flowing through a pipe with a constriction. The pipe

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 2.00 m/s and the velocity of the fluid in the narrow section of pipe is 10.0 m/s. 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)

Answer is 251 kPa

Explanation / Answer

Solution:

Given,

v1 = 10 m/s and v2 = 2 m/s.

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 30o

The narrow section is 5 m is lower than the wide section.

Now Using Bernoulli equation,

P1 + 0.5*1000*v12 + 1000*gh1 = P2 + 0.5*1000*v22 + 1000*gh2

h1 = 0 m, h2 = 5 m

P2 = 250 kPa

Substituting the values gives,

P1 = 251050 Pa = 251 kPa.

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