Fluid Mechanics Conceptual Questions 2

Write an equation that relates absolute pressure to gage pressure

Pabs = Pgage + Patm

(absolute pressure = gage pressure + atmospheric pressure)

Write down Pascal's Law.

P=F​/A

Pressure is the same in all directions in a fluid. It equals force divided by area.

Define an inviscid fluid.

A fluid with no viscosity (no internal friction).

How does density change with temperature for liquids?

As temperature increases, density decreases.

In solids, shear stress is proportional to ...

shear strain

In fluids, shear stress is proportional to ...

the rate of shear strain

What fundamental law is the basis of the energy equation?

The First Law of Thermodynamics (Conservation of Energy)

What fundamental law is the basis of the Euler Equations?

Newton’s Second Law (ΣF = ma)

What equation is obtained by integrating a Euler equation along a streamlines?

The Bernoulli Equation

Does Bernoulli equation assume inviscid form?

Yes, meaning there are no viscous forces like friction

Write down the part of the momentum equation representing “local change” for a fluid with a density ρ and a velocity v in a control volume CV with a control surface CS and a unit normal vector n. (Use arrows over variables names to denote vectors.)

Write down the part of the momentum equation representing “convective change” for a fluid with a density ρ and a velocity v in a control volume CV with a control surface CS and a unit normal vector n. (Use arrows over variables names to denote vectors.)

Write down a simplified form of the momentum equation (without any integrals) that applies to a steady, incompressible flow through a fixed (not moving) control volume with a single inflow section with an average velocity vin, a single outflow section with an average velocity v_out, a discharge Q, and a density ρ. (Use arrows over variables names to denote vectors.)

Write down a mass conservation equation for a fluid with density and velocity v in control volume CV with a control surface CS and unit outward normal vector n, (Use arrows over variable names to denote vectors)

Write down a simplified (no integrals) volume conservation equation for a cylindrical tank of diameter D filled to a depth y that is being filled by a constant discharge Q. The tank has no outflow.

When cross-sectional Area (A) decreases

speed (V) increases

Bernoulli’s Principle

Pressure is high when speed is low and vice versa

When height (h) increases

Pressure (P) decreases

Pressure is lower at higher elevation

When velocity (V) increases

Pressure (P) decreases

EGL (Energy Grade Line)

represents the total head height

HGL (Hydraulic Grade Line)

represents the sum of elevation and static pressure heads

HGL declines more rapidly than EGL

True! because some of the potential energy of the liquid is converted into kinetic energy

Pumps boost mechanical energy (through increase in pressure) so EGL and HGL rise

True