Fluid Mechanics

106 flashcards by MentisLibrary

Fluids at rest and in motion: properties and statics, the conservation laws, Bernoulli and energy, pipe and open channel flow, drag and lift, dimensional analysis, compressible flow and turbomachinery, with units on every quantity.

How do density, specific weight and specific gravity differ?
Density is mass per volume, specific weight is weight per volume, and specific gravity is the dimensionless ratio of a substance's density to that of water at 4 C.
State Newton's law of viscosity.
Shear stress in a fluid is proportional to the velocity gradient normal to the flow, with dynamic viscosity as the constant of proportionality.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity measures resistance to shear. Kinematic viscosity is dynamic viscosity divided by density, and it is what appears in the Reynolds number.
How does viscosity change with temperature for liquids and for gases?
Liquid viscosity falls sharply as temperature rises because molecules escape each other's attraction. Gas viscosity rises with temperature because molecular momentum exchange increases.
What makes a fluid non-Newtonian, and name the main types.
Its apparent viscosity depends on shear rate. Shear thinning fluids such as blood and paint get thinner as they are sheared; shear thickening fluids such as cornstarch suspensions get thicker; Bingham plastics need a yield stress before flowing at all.
What is surface tension, and where does it matter?
The energy per unit area of a liquid surface, arising from unbalanced molecular attraction at the interface. It dominates at small scales: droplets, bubbles, capillaries and menisci.
How high does water rise in a capillary tube?
In proportion to surface tension and inversely with tube diameter, so narrow tubes lift water further. The contact angle decides whether the liquid rises or is depressed.
What is cavitation, and what property predicts it?
Local boiling when static pressure falls to the vapour pressure of the liquid. The collapsing vapour bubbles pit metal surfaces and destroy pump impellers and propellers.
What does the bulk modulus of a fluid measure?
Its resistance to volume change under pressure. Water is nearly incompressible, which is why liquids transmit pressure so well and why water hammer is violent.
How is the ideal gas law used in fluid mechanics?
To relate density to pressure and temperature for a gas, which is required whenever compressibility matters. Air uses a specific gas constant of 287 J/(kg K).
What is the continuum assumption, and when does it fail?
That fluid properties can be defined at a point because the molecular mean free path is far smaller than any length scale of interest. It fails in rarefied gases and microscale flows.
Write the hydrostatic pressure equation and say what it assumes.
Pressure increases linearly with depth in a static fluid of constant density. It assumes no motion, no shear, and a fluid at rest with respect to the container.
What is the difference between gauge and absolute pressure?
Gauge pressure is measured relative to local atmospheric pressure, absolute pressure relative to a perfect vacuum. Most instruments read gauge; every gas law needs absolute.
How does a U-tube manometer measure a pressure difference?
By balancing the unknown pressure against a column of a denser fluid. The difference is the manometer fluid density times gravity times the height difference, corrected for any working fluid legs.
How do you compute the resultant hydrostatic force on a submerged plane surface?
As the pressure at the centroid multiplied by the area. The pressure distribution is linear, so its average equals the centroid value.
Where does the resultant hydrostatic force act on a plane surface?
Below the centroid, at the centre of pressure. The offset comes from the second moment of area and shrinks as the surface goes deeper.
How do you find the hydrostatic force on a curved surface?
Resolve it into components. The horizontal component equals the force on the vertical projection; the vertical component equals the weight of the fluid column above the surface, real or imagined.
State Archimedes' principle.
The buoyant force on a submerged or floating body equals the weight of the fluid it displaces, and it acts through the centroid of the displaced volume.
What determines the stability of a floating body?
The metacentric height. If the metacentre lies above the centre of gravity the body is stable, because a heel produces a righting moment.
What happens to the free surface of a fluid in a uniformly accelerating tank?
It tilts to a plane whose slope is the ratio of horizontal acceleration to the effective vertical acceleration, and lines of constant pressure run parallel to that surface.
What shape does the free surface take in a rotating cylinder of liquid?
A paraboloid. The rise at the wall equals the drop at the centre, so the volume is conserved about the original level.
What does the Reynolds transport theorem do?
It converts a system law, written for a fixed mass, into a control volume law, written for a fixed region of space. Every conservation equation in fluid mechanics comes from it.
Write the steady flow continuity equation for a stream tube.
Mass flow in equals mass flow out. For incompressible flow the density cancels and volumetric flow is conserved.
Write the steady momentum equation for a control volume.
The net external force equals the momentum flux out minus the momentum flux in. It is a vector equation, so it must be applied component by component.
How do you find the force on a pipe bend?
Draw a control volume cutting the pipe at inlet and outlet, include the pressure forces on both cut faces, and solve the momentum equation for the anchoring force.
What force does a jet exert on a stationary flat plate held normal to it?
The plate must absorb the entire axial momentum flux, so the force equals mass flow times jet velocity, or density times area times velocity squared.
What does the angular momentum equation add for turbomachinery?
It relates torque to the change in the moment of momentum between inlet and outlet, which is exactly what a rotor does. That gives the Euler turbomachine equation directly.
Write the steady flow energy equation in head form.
Total head at the inlet plus pump head equals total head at the outlet plus turbine head plus losses. It is Bernoulli's equation with real machinery and friction restored.
What is the difference between a streamline, a pathline and a streakline?
A streamline is tangent to the velocity field at one instant, a pathline is the trajectory of one particle over time, and a streakline joins all particles that passed one point. In steady flow all three coincide.
What is the difference between the Eulerian and Lagrangian descriptions?
Eulerian watches fixed points in space and records what passes; Lagrangian follows individual fluid particles. Most fluid mechanics is Eulerian because instruments sit still.