Fluid Dynamics and Bernoullis Equation Questions and Answers

Answer: C

An assumption of Bernoulli's equation is that the flow is steady.

Bernoulli's equation is derived by integrating Euler's equation along a streamline, assuming the flow is steady, the fluid is ideal (non-viscous) and incompressible, and the flow is irrotational (or the equation is applied along one streamline).

So rotational, compressible and turbulent flow all contradict its assumptions: compressibility needs a different energy equation, and turbulence brings losses and unsteadiness the simple equation ignores.

Answer: A

Piezometric head is the sum of datum head and pressure head.

Piezometric head is \(z + p/w\), the height to which liquid would rise in a piezometer tube above the datum. It is the level of the hydraulic gradient line.

Adding velocity head \(V^2/2g\) to it gives the total head (the energy line), which is what the third option describes, so it is not the definition of piezometric head itself. Datum head plus velocity head leaves out pressure, and 'piezometric head plus dynamic head' is again total head.

Answer: B

An assumption of Bernoulli's equation is that the fluid is incompressible.

The standard derivation from Euler's equation along a streamline assumes the fluid is ideal (non-viscous) and incompressible, the flow is steady, and, when applied between any two points rather than along one streamline, the flow is irrotational.

The other options reverse these conditions: the flow is assumed irrotational, not rotational, and steady, not unsteady. 'Ideal plastic' describes a solid that yields at constant stress, not a fluid at all.

Answer: D

Flow is inviscid when the viscous force is negligible.

An inviscid (ideal) fluid is one treated as having zero viscosity, so there are no shear stresses within it. Real flows behave this way away from solid walls and at high Reynolds number, where inertia forces dominate viscous forces. Euler's equation and Bernoulli's equation are derived on this assumption.

Neglecting gravity, inertia or pressure forces does not make a flow inviscid. Inertia and pressure are the very forces that remain in Euler's equation once viscosity is dropped, and gravity appears in Bernoulli's equation as the elevation head.