internal flows

What is an internal flow?

A flow whose downstream development is confined or altered by surrounding boundaries.

Give examples of internal flows.

Fuel lines, hydraulic systems, pneumatic systems, wind tunnels, cooling systems, engine ducts.

What is the primary difference between internal and external flows?

In internal flows boundary layers eventually affect the entire flow field.

Why do internal flows experience pressure losses?

Viscous friction along the walls dissipates energy.

What are the four common categories of internal-flow problems?

Pressure drop, flow rate, pumping power, and pipe sizing.

What is entrance length?

The distance required for flow to become fully developed.

What defines a fully developed flow?

The velocity profile no longer changes in the flow direction.

What is the laminar entrance-length relation?

Le/D ≈ 0.05Re.

What is the turbulent entrance-length relation?

Le/D ≈ 4.4Re^(1/6).

What Reynolds number is used for pipe flow?

Re = ρVD/μ.

When is pipe flow typically laminar?

Re < 2300.

When is pipe flow typically turbulent?

Re > 4000.

What is hydraulic diameter?

Dh = 4Ac/P.

Why is hydraulic diameter used?

To analyze non-circular ducts using pipe-flow correlations.

What is Hagen-Poiseuille flow?

Fully developed laminar flow through a circular pipe.

What is the velocity profile for laminar pipe flow?

Parabolic.

Where is the maximum velocity in a laminar pipe?

At the centerline.

How does maximum velocity compare to average velocity in laminar pipe flow?

Vmax = 2Vavg.

What is Poiseuille's Law?

Q = (Δp πD⁴)/(128μL).

What does Poiseuille's Law show about diameter?

Flow rate scales with D⁴.

What is the Darcy-Weisbach equation?

Δp = f(L/D)(ρV²/2).

What is the friction factor for laminar flow?

f = 64/Re.

What is head loss?

Equivalent height corresponding to pressure loss.

Relationship between head loss and pressure drop?

hL = Δp/(ρg).

General pumping-power equation?

P = QΔp.

How does pipe roughness affect pressure loss?

Increased roughness increases friction factor and pressure loss.

What is relative roughness?

ε/D.

What determines friction factor in turbulent flow?

Reynolds number and relative roughness.

What equation determines turbulent friction factor?

Colebrook-White equation.

Why is the Colebrook-White equation difficult to solve?

It is implicit in friction factor f.

What chart is used for turbulent pipe-flow calculations?

Moody Chart.

What does the Moody Chart provide?

Friction factor as a function of Reynolds number and relative roughness.

What happens to friction factor as roughness increases?

It increases.

What happens to pressure losses as roughness increases?

They increase.

What is the hydraulically rough regime?

A regime where friction factor depends primarily on roughness and not Reynolds number.

What is cavitation?

Vapor bubble formation caused by pressure dropping below vapor pressure.

Why is cavitation dangerous?

It causes noise, vibration, efficiency loss, and damage.

What does NPSH stand for?

Net Positive Suction Head.

How can cavitation be prevented?

Ensure NPSH available exceeds NPSH required.

What is a local loss coefficient?

K.

Pressure loss through a fitting or bend?

Δp = K(ρV²/2).

How do sharp bends affect pressure loss?

They increase pressure loss significantly.

How can bend losses be reduced?

Use smoother bends with larger radii.

What is the mechanical-energy equation used for?

Combining pressure, velocity, elevation, pump head, and losses.

Why are turning vanes used in wind tunnels?

To reduce corner losses and guide flow smoothly.

What is Fanno flow?

Adiabatic compressible flow in a constant-area duct with friction.

How does friction affect subsonic Fanno flow?

Mach number increases toward 1.

How does friction affect supersonic Fanno flow?

Mach number decreases toward 1.

What happens to stagnation pressure during Fanno flow?

It decreases.

What happens to stagnation temperature during Fanno flow?

It remains constant.

What is choking in Fanno flow?

The flow reaches Mach 1 and maximum mass flow.

Why can't mass flow increase after choking?

Mach 1 limits further increases under the given conditions.

How does increasing duct length affect choking?

It moves the flow closer to choking.

How does increasing friction factor affect choking?

It causes choking to occur sooner.