Fluid Mechanics Study Notes

A set of Q&A flashcards covering key concepts from the Fluid Mechanics lecture notes.

What is the difference between a solid and a fluid?

A fluid moves and continually deforms under shear stress; a solid deforms under shear stress but does not flow.

What does viscosity represent, and how does temperature affect it?

Viscosity represents resistance to flow; it decreases as temperature increases.

How do temperature and pressure affect density and viscosity?

Density changes with temperature and pressure; viscosity is a function of temperature only.

What is the continuum assumption in fluid mechanics?

A continuous mass over the whole space; sample is large enough so every property is present.

What is the difference between gauge pressure and absolute pressure?

Gauge pressure is measured relative to atmospheric; absolute pressure is measured with respect to zero; Pabs = Pgauge + atm.

What is the relationship between density and unit weight (specific weight)?

Specific weight γ = ρ g; density relates by γ = ρ g (i.e., γ is density times gravity).

What is the definition of specific gravity?

SG = (density / specific weight of fluid) / (density / specific weight of water); equivalently SG = ρ/ρ_water.

What is the relation between vapor pressure and boiling point?

Boiling occurs where local pressure equals vapor pressure.

What is cavitation?

Localized low-pressure zones cause vapor bubbles to form and grow, then collapse in higher downstream pressure.

Name three properties of pressure.

Pressure acts in all directions; pressure is normal to surfaces; fluid transmits pressure.

Where is the buoyant force applied on a submerged object?

Buoyant force is vertical and acts at the center of buoyancy (the centroid of displaced fluid).

Define P, pressure head, piezometric pressure, and piezometric head as given in the notes.

P = ρ g y; Pressure head = y = P/(ρ g); Piez pressure = P + ρ g z; Piez head = P/(ρ g) + z.

What is the relative location of the center of area and the center of pressure?

Center of pressure acts below the center of area.

What is a streamline?

Line drawn through the flow field so that the local velocity is tangent to the streamline at every point along the line.

What are the different components of acceleration?

Local (dV/dt); Convective (V*(dV/ds)); Centripetal (V^2/r).

What is ideal fluid, irrotational flow, non viscous, and steady flow?

Ideal fluid: incompressible, irrotational, non-viscous, steady flow. Irrotational flow: fluid elements do not rotate. Non-viscous: no internal friction. Steady flow: velocity is constant at each point in time.

Irrotational, stagnation pressure holds constant on the streamline and between any two points in the fluid

Stagnation pressure is constant along a streamline and between any two points in an irrotational, non-viscous fluid.

Bernoulli's equation along a streamline versus any two points in the flow field

Along a streamline, Bernoulli applies between two points on that streamline; between two arbitrary points, it can apply if the flow is irrotational and non-viscous.

If the pressure reduces in a flow, does it mean that the velocity has to increase?

Yes—the velocity increases to keep the total energy constant.

What is stagnation pressure?

P0 = P + ½ ρ V^2.

Meaning of each term in the Bernoulli equation

P – pressure term; ρ g z – weight/elevation term; ½ ρ V^2 – kinetic energy term.

What is the basic assumption involved in the Euler equation?

Friction is neglected (inviscid flow).

What is the relationship in the rotating fluid at the center versus outside

Pressure is less in the middle than on the outside.

Under what conditions does mass conservation reduce to volume conservation?

The fluid is incompressible (density is constant).

What is a control volume?

A volume located in space through which matter can pass (steady flow and uniform velocity); a region for observation.

What are the direction and orientation of the unit normal vector?

Perpendicular and pointed outward from the inlets and outlets.

What is inertial frame of reference?

Non-accelerating and non-rotating frame of reference.

What forces should be considered in the momentum principle?

Weight; friction force; pressure force.

Momentum flux coefficient, why is it needed and how is it calculated?

It accounts for the velocity profile (non-uniform flow); calculated as ∫(u^2 dA)/(A V^2).

The meaning of the terms in the energy equation (alpha*V^2)/(2g) - KE flux, Z - PE flux, P/(ρ)g - rate of work by pressure, hf - energy loss due to friction, hp - energy transferred to fluid by pump, ht - energy transferred to turbine

KE flux: α V^2/(2g); PE flux: Z; work by pressure: P/(ρ)g; friction loss: hf; pump energy: hp; turbine energy: h_t.

What is alpha and how is it calculated?

Kinetic energy correction factor α = (1/A) ∫(V/V̄)^3 dA.

How do you convert a head into power?

Multiply the head by ρ Q g (or ṁ g).

What do energy grade line and hydraulic grade line represent?

EGL = P/(ρ g) + z + α V^2/(2g); HGL = P/(ρ g) + z.

What term in the energy equation represents change in heat and internal energy terms?

(i2 - i1)/g − Q̇ h = h_f.

Why is dimensional analysis important?

Helps identify the most important parameters and reduce the number of experiments.

What are the rules for selecting repeating variables?

Select k variables out of m variables so that they cannot form a dimensionless group.

What are the primary dimensions?

Mass (M), Length (L), Time (T).

What is similitude and how do we achieve it?

Predict prototype performance from model tests; Geometric: exact geometric replica; Dynamic: dominant forces in model and prototype are in the same ratio; Kinematic: geometric and dynamic conditions are satisfied.

How does friction loss vary with pipe diameter and velocity?

As diameter increases, hf decreases; as velocity increases, hf increases; hf = f L V^2 /(2 g D).

What are components of head loss?

Friction losses (hf) and local losses (hk).

What are some of the minor losses in the pipe system?

Valves, pipe constriction/expansion, bends, entrance/exit losses.

What is the physical difference between laminar and turbulent flow?

Laminar flow is smooth and layered; turbulent flow is chaotic with eddies and unsteady motion.

What type of flow is more conductive to mixing?

Turbulent flow produces higher mixing; velocity profile is more uniform than in laminar flow.

When does friction factor become independent of Reynolds number?

In fully rough turbulent flow.

How do we differentiate between laminar and turbulent flow based on Reynolds number?

Laminar: Re ≤ 2000; Turbulent: Re ≥ 3000.

t = u(dV/dy) is valid for which type of flow?

Laminar flow.

Uniform and non-uniform flow in open channels.

Uniform flow: velocity constant along a streamline, depth and cross-section constant along the length; bed and water surface parallel; HGL, EGL, and bed are parallel; Sf.

Non-uniform flow: definition?

Velocity changes from section to section along the channel; depth varies along the channel.

What are subcritical, supercritical, and critical flows based on Froude number and diagram?

Supercritical: depth < critical (velocity > critical); Subcritical: depth > critical (velocity < critical); Critical: specific energy minimum with a unique depth.

What are mild slope, steep slope, and critical slope?

Mild: So > yc and Fr < 1; Steep: So < yc and Fr > 1; Critical slope yields critical flow.

What is the best hydraulic or most efficient section?

Geometry yielding a minimum wetted perimeter for a given area, minimizing viscous energy loss.

How can hydraulic radius be a measure of channel efficiency?

Hydraulic radius RH = Awetted / Pwetted; higher RH generally indicates more efficient flow.

What is a hydraulic jump?

A transition from supercritical upstream to subcritical downstream flow.

Where can critical flow occur?

On the energy/specific energy diagram at a minimum specific energy (between mild and steep).

What is the condition for maximum possible upward step in an open channel without changing upstream flow conditions?

E1 = E2 + ΔZ with E1 > E2; using the Froude relation to find critical depth Yc; V^2 = g Yc; E2 = y + 0.5 y^2.

What is the condition for the maximum constriction in an open channel without changing the upstream flow conditions?

Fr = 1 (critical flow).

When solving energy equation, how do you select the right flow depth?

For supercritical flow, choose the lower depth from the three roots; for subcritical flow, choose the higher depth.

Know E-y diagram for a given discharge and y-q diagram for a given discharge.

E-y diagram shows the relationship between depth and specific energy; y-q diagram shows depth for a given discharge.