Question

In which scenario is Bernoulli's equation modified to include a term for head loss?

• A. Inviscid, compressible flow
• B. Incompressible, inviscid flow
• C. Turbulent, viscous flow
• D. Steady, uniform flow

Hint:

Modified Bernoulli Equation. For real (viscous) flows, the standard Bernoulli equation is modified by adding a head loss term (\(h_L\)) to account for energy dissipation due to friction. This is particularly important for turbulent flows.

Answer 1

The Correct Option is C

The standard Bernoulli equation is derived assuming ideal flow conditions, including inviscid (frictionless) flow.
In real fluid flows, particularly those that are viscous and/or turbulent, energy is lost due to friction between fluid layers and between the fluid and pipe walls.
This energy loss manifests as a pressure drop or "head loss" (\(h_L\) or \(h_f\)).
To apply the principle of energy conservation to real flows, the Bernoulli equation is modified to include this head loss term, often written as: $$ \frac{P_1}{\rho g} + \frac{v_1^2}{2g} + z_1 = \frac{P_2}{\rho g} + \frac{v_2^2}{2g} + z_2 + h_L $$ This head loss is significant in viscous flows and especially in turbulent flows.
Option (2) represents the ideal conditions where the standard Bernoulli equation applies without a head loss term.
Compressibility (Option 1) requires further modifications or use of different energy equations.
Steady, uniform flow (Option 4) doesn't automatically imply the need for head loss, although it might be present.
The presence of viscosity and turbulence (Option 3) necessitates the inclusion of the head loss term.