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A liquid is flowing through a horizontal cylindrical vessel pipe which has a wide section at position 1 and a narrow section at position 2.  Assume that the flow is frictionless.Which of the following is most correct?Question 8Select one:a.The pressure at position 2 is lower than the pressure at position 1 - but by how much depends only on the liquid's density.b.The pressure at position 2 is lower than the pressure at position 1 - but by how much depends only on the liquid's flow speed.c.The pressure at position 2 is lower than the pressure at position 1 - but by how much depends on both the liquid's density and flow speed.d.The pressure at position 2 is higher than the pressure at position 1 - but by how much depends on both the liquid's density and flow speed.

Question

A liquid is flowing through a horizontal cylindrical vessel pipe which has a wide section at position 1 and a narrow section at position 2.  Assume that the flow is frictionless.Which of the following is most correct?Question 8Select one:a.The pressure at position 2 is lower than the pressure at position 1 - but by how much depends only on the liquid's density.b.The pressure at position 2 is lower than the pressure at position 1 - but by how much depends only on the liquid's flow speed.c.The pressure at position 2 is lower than the pressure at position 1 - but by how much depends on both the liquid's density and flow speed.d.The pressure at position 2 is higher than the pressure at position 1 - but by how much depends on both the liquid's density and flow speed.

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Solution

The correct answer is c. The pressure at position 2 is lower than the pressure at position 1 - but by how much depends on both the liquid's density and flow speed.

This is based on Bernoulli's principle, which states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.

According to Bernoulli's principle, the total energy in a steadily flowing fluid system is conserved. The energy in a fluid, per unit volume is in the form of pressure energy, kinetic energy and potential energy.

In the case of a horizontal pipe with varying cross-sectional area, the fluid will flow faster in the narrower sections (position 2) and slower in the wider sections (position 1). As the fluid speeds up, its pressure decreases; and as it slows down, its pressure increases.

The change in pressure between two points in a fluid is not only dependent on the change in speed of the fluid, but also on the density of the fluid. Hence, the pressure at position 2 is lower than the pressure at position 1, and the difference depends on both the liquid's density and flow speed.

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