In steady laminar flow inside a pipe, how does the velocity vary across the pipe's cross-section?

Velocity is uniform across the entire cross-section It forms a parabolic profile — fastest at the centre and zero at the pipe wall Velocity is fastest near the walls due to boundary friction heating the fluid Velocity increases linearly from zero at one wall to maximum at the opposite wall

Turbulent flow differs from laminar flow in that it:

Flows only at very low velocities and high viscosities Has chaotic, irregular motion with eddies and mixing between fluid layers Has a perfectly parabolic velocity profile at all times Occurs only in gases, never in liquids

The Reynolds number is defined as Re = ρvL/μ. What does it physically represent?

The ratio of the fluid's density to that of water The ratio of the pipe's diameter to the fluid's velocity The ratio of inertial forces to viscous forces in the flow The ratio of pressure forces to gravitational forces

Water flows at 2 m/s through a pipe of diameter 0.1 m (ν = 1×10⁻⁶ m²/s). What is the Reynolds number, and is the flow laminar or turbulent?

Re = 200 — laminar flow Re = 2,000 — transitional flow Re = 200,000 — turbulent flow Re = 2,000,000 — supersonic flow

The continuity equation for incompressible flow states A₁v₁ = A₂v₂. What does this mean physically?

Fluid accelerates in wider sections of the pipe to maintain momentum The same volume of fluid must pass through any cross-section per second, so narrowing the pipe speeds the flow Pressure doubles whenever the pipe cross-sectional area doubles Fluid temperature remains constant along the pipe regardless of diameter changes

Bernoulli's equation (P + ½ρv² + ρgh = constant) applies to flow that is:

Turbulent, compressible, and viscous Unsteady, incompressible, and inviscid across any flow cross-section Steady, incompressible, and inviscid (frictionless) along a streamline Any flow where the fluid temperature is constant

A Venturi meter works by measuring pressure drop in a narrowed section of pipe. Using Bernoulli's principle, what does a lower pressure in the narrow throat indicate?

Lower flow velocity in the throat due to increased friction Higher flow velocity in the throat, which can be used to calculate the volume flow rate A reversal of flow direction caused by the narrowing Increased fluid density as the pipe narrows

A pitot tube on an aircraft measures airspeed by:

Measuring the temperature difference between the front and rear of the tube Counting how many air molecules strike a sensor per second Comparing stagnation pressure (where flow is stopped) to static pressure; the difference is dynamic pressure, giving speed Measuring the frequency of turbulent eddies shed behind the tube

The stagnation point on a body immersed in a flow is where:

The fluid velocity is highest and pressure is lowest Turbulent separation from the surface first occurs The fluid velocity is zero and pressure is at its maximum on the body surface The boundary layer transitions from laminar to turbulent

The boundary layer is:

The outermost layer of the fluid where turbulence is greatest A thin region of slower fluid adjacent to a surface where viscous effects are significant The interface between two fluids of different densities The zone in a pipe where flow transitions from laminar to turbulent

Pressure (form) drag on a blunt body is caused by:

High-speed flow rubbing against the body surface, creating friction A low-pressure wake behind the body where the boundary layer has separated Compressibility effects when air is squeezed against the front of the body Gravity pulling the body downward through the fluid

A perfume atomiser (spray bottle) works by Bernoulli's principle. How?

Squeezing the bulb creates high pressure that pushes the liquid up the tube by Pascal's law Squeezing the bulb creates fast-moving air over the tube opening, lowering the pressure and drawing perfume up into the airstream The liquid is heated by friction, vaporises, and rises as a gas Surface tension pulls the liquid up the tube when the cap is removed