In streamline flow through a horizontal pipe of uniform cross section, Bernoulli's equation predicts that the pressure
Correct answer: B. stays the same along the pipe for an ideal fluid
- A. rises steadily along the pipe
- B. stays the same along the pipe for an ideal fluid
- C. falls to zero at the outlet
- D. depends on the colour of the pipe
Explanation
With constant area the speed is constant by continuity, and with no height change the potential term is constant too, so the pressure term must also be constant for an ideal fluid. Real fluids do lose pressure along such a pipe because viscosity dissipates energy, which is exactly the effect Bernoulli's equation leaves out. Comparing the ideal prediction with the real behaviour is how the role of viscosity is demonstrated.
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About Bernoulli's Equation
Bernoulli’s equation applies conservation of energy to steady flow of an incompressible, non-viscous fluid along a streamline: pressure, kinetic and gravitational terms have a constant total. It explains pressure-speed changes in narrow pipes, Venturi meters and lift, and differs from continuity because it relates pressure as well as velocity and height.
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