4. Fluids EQUATIONS

Question 1

4 (Equation) What is the equation for Density?

Answer 1

ρ=density
m= mass
V= volume

Question 2

4(Equation) Weight of a fluid.

Answer 2

F_g=ρVg

or F_g=gm

Note= the difference in these equations is that in the first one, you don’t know the mass but you know density (taken from the density equation of p=m/v), and in the second one you do know the equation.

F_g= weight
ρ = density
V=volume
g= acceleration due to gravity (9.8 or 10m/s²)

Question 3

4 (Equation) What is the equation for specific gravity?

Answer 3

ρ=density of substance over the specific gravity of water

** The value of SG is going to be unitless. It just tells you if it will float or not. If it is greater than 1, it will sink in water. If it is less than 1, it is less dense and it will float.

Question 4

4 (Equation) What is the equation for pressure?

Answer 4

P=pressure

• Units for pressure= pascal (Pa) which equals
• 1Pa= 1 N/m²=
• 1atm= 760 torr= 760 mmHg =110,130 Pa

F=force (N)
A= area (m²)

Question 5

4 (Equation) What is the equation for hydrostatic pressure?

Answer 5

P=P_o + ρgz

• P=absolute pressure
• P_o= incident or ambient pressure (does not always mean ambient pressure, however, in general, 1 atm)
• ρ= density of the fluid
• g= acceleration due to gravity (9.8 m/s²)
• z= depth of the object

Question 6

4 (Equation) What is the equation for gauge pressure?

Answer 6

It’s important to note that because the Incident or ambient pressure generally equals the atmospheric pressure, the equation just results to P_gauge= ρgz

The longer version of this is:
P_gauge=P-P_atm= (P_o +ρgz)-P_atm

• P_gauge= pressure of the gage
• P= total pressure
• P_atm= pressure outside the closed system
• P_o= incident or ambient pressure (does not always mean ambient pressure, however, in general, 1 atm)
• ρ= density of the fluid NOT object
• g= acceleration due to gravity
• z= depth of the object

Question 7

4 (Equation) What is application of Pascal’s law to hydraulic machine and mechanical advantage?

Answer 7

P= pressure
F₁=downward force on piston 1
A₁= Surface area of piston 1
F₂= the upward force on piston 2
A₂= the surface area of piston 2

Similar the the equation F=W=P∆V in that P=W/∆V

Question 8

4 (Equation) What is the equation for Buoyance?

Answer 8

F_buoy=ρ_fluid V_{fluid displaced} g= ρ_fluidV_submerged g

F_g,b= m_bg=ρ_bV_bg

F_buey= upwards
ρ_fluid= density of fluid (NOT DENSITY OF OBJECT)
V_{fluid displaced}=fluid displaced
g= force exerted by gravity
ρ_fluid = density of fluid displaced (NOT DENSITY OF OBJECT)
V_submerged =volume of the object submerged

Question 9

4 (Equation) What is the equation to calculate the rate of flow through a pipe or confined space?

Answer 9

• Q= flow rate (volume flowing per time)
• r= radius of the tube
• ∆P= the pressure gradient
• η= viscosity of the fluid
• L=length of the pipe

Key Point: The MCAT really will not test on this equation. However, it does want you to know that the flow will increase if the radius increases (by an exponent of 4). So it’s important to know that a slight change in the radius may have a significant effect on the pressure gradient.

Question 10

4 (Equation) What is Bernoulli’s equation for static pressure and dynamic pressure?

Answer 10

• P= absolute pressure of the fluid
• ρ= density of the fluid
• v= linear speed
• g= the acceleration due to gravity
• h= the height of the fluid above some datum

Pressure + KE + Potential Energy= Pressure + KE + Potential Energy

Key Point: in the end, Bernoulli’s equation is nothing other than a statement of energy conservation: more energy dedicated toward fluid movement means less energy dedicated toward static fluid pressure. Also, the inverse is true: more static pressure means less movement.

If they are the same height you can ignore the ρgh because they will be the same on both sides

It tells us that when the liquid speeds up, its pressure goes down.

Question 11

4 (Equation) What is the equation that compares area and flow in a tube? i.e. when one tube increases in diameter, what happens to the speed of the flow?

Answer 11

Q=A₁v₁=A₂v₂

A= area (remember, area = πr²
v= speed in m/s