Fluids and solids Flashcards
Give the formula for density. Is this definition true for all states of matter?
Density = mass/volume
True for solids, fluids and gases (all phases).
What is specific gravity (SG) and how is it calculated?
SG = (density of a substance)/(density of water)
Often the same as its density due to the fact that the density of water is about 1 g/mL
SG is dimensionless (no units) and therefore a good standard measure of relative density
Define pressure
Pressure is defined as the force (F) per unit area (A)
P = F/A
The force (F) is the normal (perpendicular) force to the area.
The SI unit for pressure is the pascal (1 Pa = 1 N/m^2)
Give the formulations of pressure for potential energy/unit volume (5)
P = F/A = mg/A = (mg/a)/(h/h) = mgh/v = pgh
p = density h = depth below surface
What are 6 characteristics of force and pressure on incompressible liquid fluids?
- Forces exerted by fluids are always perpendicular to the surface of the container
- The fluid pressure (hydrostatic) is directly proportional to the depth of the fluid and to its density
- At any particular depth, the pressure of the fluid is the same in all directions
- Fluid pressure is independent of the shape or area of its container
- An external pressure applied to an enclosed fluid is transmitted uniformly throughout the volume of the liquid (Pascal’s law)
- An object which is completely or partially submerged in a fluid experiences an upward force equal to the weight of the fluid displaced (Archimedes’ principle)
How can Archimedes principle be used to calculate specific gravity? If SG = 0.90, how much of the object is below the surface of water?
Specific gravity is equivalent to the fraction of the height of a buoyant object below the surface of the fluid.
Thus, if SG = 0.90, then 90% of the height of the object would be immersed in water.
Therefore, less dense objects float
Give the units and equivalencies for pressure in SI, atm, bars, mmHg torr and imperial
SI: 1 Pa = 1 N/m^2
1.00 atm = 1.01x10^5 Pa = 1.01 bar = 760 mmHg = 760 torr = 14.7 lb/in^2
What two equations describe fluids in motion? Describe fluids in motion in terms of streamline and turbulent flow.
- The continuity equation
- Bernoulli’s equation
Fluids in motion are assumed to have streamline (laminar flow) which means that the motion of every particle in the fluid follows the same path. Turbulent flow occurs when that definition cannot be applied (resulting in energy dissipation from collisions and increase in frictional drag)
What is viscosity (η)? What is it measuring?
Analogous to friction between moving solids. It is resistance to flow (for layers of a fluid in streamline flow) past each other.
Viscosity (η) results in dissipation of mechanical energy. As one layer flows over another, the second is set into motion as energy is transmitted to it (transfer of momentum)
The greater the transfer of this momentum from one layer to another, the more energy that is lost and the slower th layers move.
η is the measure of the efficiency of transfer of this momentum.
What does a high viscosity coefficient (η) indicate about a fluid?
Higher transfer of momentum and greater loss of mechanical energy (and thus loss of velocity)
How can the streamline or turbidity of a fluid in motion be measured?
Reynold’s Number (R)
R = vdρ / n
v: velocity of flow
d: diameter of the tube
ρ: density of the fluid
η: viscosity coefficent
laminar flow occurs when R < 2300 and turbulent flow occurs when R > 4000. In the interval between 2300 and 4000, laminar and turbulent flows are possible and are called “transition” flows, depending on other factors, such as pipe roughness and flow uniformity.. As v, d, ρ and/or η increases, the flow becomes more turbulent.
Describe cohesive and adhesive forces of fluids
Cohesive forces: fluid molecules attract each other
Adhesive forces: attractive forces between fluid and surface
If a liquid is lining an object, cohesive forces cause the molecules to retract to the smallest possible surface area. What is the consequence of this?
(give two formulas for surface tension)
This creates a potential energy present in the surface.
This is proportional to the surface area (A)
Ep = γA
γ: surface tension = Ep/A = joules/m^2 or γ = F/I F: force of contraction of the surface I: length along surface
If a tube is inserted into a body of fluid, what will happen if:
cohesive forces > adhesive forces
cohesive forces < adhesive forces
cohesive forces > adhesive forces
- Liquid is lower in tube relative to surface of body of fluid
adhesive forces < cohesive forces
- Liquid is higher in tube relative to surface of body of fluid
What is stress on solid objects defined as? Give the definition of the modulus of elasticity (ME)
The ration of the force to the area over which it acts.
ME = Stress/strain
Strain is defined as the relative change in dimensions or shape of an object caused by stress
List three types of stress on solid objects
- Tensile stress
- Compressive stress
- Shearing stress
- Tensile stress
- Compressive stress
- Shearing stress
Give the two commonly used moduli of elasticity for solid objects
- Young’s Modulus (Y) for compressive or tensile stress
Y = (longitudinal stress)/(longitudinal strain) Y = (F/A)/(ΔI/I) = (FxI)/(AΔI)
Where I = length
- Shear modulus (S) or the modulus of rigidity
S = shearing stress/shearing strain S = (F/A)/tanΦ
There are two liquids in two containers. The second liquid is twice as dense as the first one.
Pressure measurements at different depths are taken for the first liquid:
- 5 cm depth = 250 N/m^2 pressure
- 10 cm depth = 450 N/m^2 pressure
What is the pressure of the second liquid at a depth of 10 cm?
Because the density is twice as much, the pressure due to gravitational forces of the liquid is twice is much. However, the data implies an extra pressure of 50 N/m^2 at zero depth, so this must be added (400 x 2 + 50 = 850).
850 N/m^2 is the answer.
An object with 15 grams mass is immersed in benzene and suffers an apparent loss of mass of 5 grams. What is the approximate specific gravity of the object? (Specific gravity of benzene = .7)
2.1
The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object (Archimedes’s principle).
There were 5g of liquid displaced, thus the ratio of object mass to fluid mass is 15/5 = 3. The specific gravity of the object (mass per unit volume compared to water) is three times the specific gravity of bense (3 x .7 = 2.1) because the volumes of object and displaced liquid are equal.
As a balloon rises in water, the temperature of the gas inside falls. Why is this?
As the pressure in the balloon decreases, the gas expands and does work on the balloon/water, thereby decreasing its internal energy.
A large cylindrical concrete tank is filled with water and has a horizontal facing near the bottom. If the valve is opened to drain the tank, where is the speed of the flowing water the greatest?
At the narrowest end of the pipe.
For a given volume flow rate, the speed of fluid flow is inversely proportional to the cross-sectional area through which the fluid flows.
Continuity equation:
A1v1 = A2v2
Give Archmide’s principle.
In physics problems, this principle allows you to substitute m and F for ___, ___ and ____?
If an object is floating on or immersed in a fluid, then the fluid exerts an upward buoyant force given by:
F = ρVg
v = volume of displaced fluid
m = ρV F = PA F(buoyant) = ρVg
When you are presented with a problem where something is floating in a fluid, how can you determine it’s specific gravity?
- Write a force equation (F = mg, which becomes 0 = F - mg)
- Replace m with ρV of object and replace buoyant force with ρVg of water)
0 = ρ(water)V(displaced)g - ρVg
- Express amount of water displaced as fraction (eg. 2/3 for 2/3 submerged) and cancel out V and g
0 = ρ(water)(fraction) - ρ(object)
ρ(object)/ρ(water) = fraction
ρ(object)/ρ(H20) = specific gravity
What is gauge pressure?
Most pressure that isn’t measuring the atmospheric pressure in some way is measured as gauge pressure. This includes things like blood pressure and the pressure in a column of water.
Eg. The blood pressure of a woman with a systolic blood pressure of 110 torr at standard conditions is actually 870 torr (110 + 760)
P(gauge) = P - P(atm)
