Fluid Mechanics Flashcards

A pipe suddenly expands from a diameter of 0.1 m to 0.2 m. If the velocity in the smaller pipe is 4 m/s, what is the head loss due to the sudden expansion?

Answer: 0.046 m

Using the Borda-Carnot equation: hL = (V1 - V2)²/2g; V2 = 4×(0.1/0.2)² = 1 m/s; hL = (4-1)²/(2×9.81) ≈ 0.459 m.

Which dimensionless number represents the ratio of inertial forces to viscous forces in fluid flow?

Answer: Reynolds number

The Reynolds number (Re = ρVL/μ) is the ratio of inertial to viscous forces and governs laminar vs. turbulent flow.

For a Newtonian fluid, the shear stress is proportional to:

Answer: The velocity gradient

For a Newtonian fluid, τ = μ(du/dy), where shear stress is directly proportional to the velocity gradient.

Water flows at 2 m/s through a 0.05 m diameter pipe. What is the approximate Reynolds number? (kinematic viscosity ν = 1×10⁻⁶ m²/s)

Answer: 100,000

Re = VD/ν = 2 × 0.05 / (1×10⁻⁶) = 100,000.

The hydraulic radius of a flow cross-section is defined as:

Answer: The cross-sectional area divided by the wetted perimeter

Hydraulic radius Rh = A/P, where A is cross-sectional area and P is the wetted perimeter.

In a manometer, two fluids of specific gravities 0.8 and 13.6 are used. If the manometer reads a height difference of 0.1 m of the heavier fluid, what is the differential pressure?

Answer: 13,341 Pa

ΔP = ρgh = 13,600 × 9.81 × 0.1 = 13,342 Pa ≈ 13,341 Pa using mercury (SG=13.6).

Which equation expresses conservation of energy for steady, incompressible flow along a streamline including head losses?

Answer: Modified Bernoulli equation

The modified (extended) Bernoulli equation adds pump head, turbine head, and head losses to the standard energy balance.