Review Session 8
Force of one surface
𝐹𝑇 = 𝛾𝐿
L = length of surface touching wire
𝛾 = surface tension in N/m (depends on interface)
Potential Energy of Surface
𝑈 = 𝛾𝐴
A = area of surface
Liquids try to adopt smallest surface area. Usually in form of
sphere.
Laplace Equation
𝑃𝑖𝑛 − 𝑃𝑜𝑢𝑡 =
2𝛾
𝑅
In = concave
Out = convex
Capillary Rise
ℎ=
2𝛾
𝜌𝑔𝑅
Ideal Gas Laws
𝑃𝑉 = 𝑁𝑘𝐵 𝑇
𝑃𝑚 = 𝜌𝑅𝑇
𝑅 = 𝑁 ∗ 𝑘𝐵
𝑘𝐵 = 1.38 ∗ 10−23
𝐽
𝐾
Pressure-height relationship
−ℎ
𝑃(ℎ) = 𝑃(0)𝑒 𝐻
H = height of atmosphere ≈ 8000 m
Continuity Equation
𝑄 = 𝐴1 𝑣1 = 𝐴2 𝑣2
1. You have a cross-section of a tank filled with an unknown
liquid (ρ = 1300 kg/m3), as shown below. The tank is quite
tall (h = 10 m), and it is open at the end of a tube at the
bottom.
a. What is the pressure at point b, which is halfway down
the tank?
b. If a curved surface appears as shown in the image above
in the tube at the bottom of the tank, what must be the
surface tension (N/m) of the liquid?
2. You stick a tube (R = 0.5 cm) into a bowl
of water (γ = 0.075 N/m).
a. How high does the water rise in
tube ?
b. You move to the moon (g = 1.6 m/s2) and try the same
thing. How high does the water rise in the tube on the
moon?
c. You fly back to earth and stick a thicker tube (R = 4 cm)
into the water. How high does the water rise in this
tube?
d. On earth, you now stick a tube (R = 0.5 cm) into a bowl
of an unknown liquid (ρ = 13600 kg/m3) and it rises
1.45 mm in the tube. What is the surface tension (N/m)
of the liquid?
3. You have water flowing through a tube that sits on a table.
The water has a linear velocity v at the point shown. At the
end of the tube, the water flows out off the table. Derive an
expression to model the distance, L, the water travels from
the bottom of the table.
4. To supply a dog’s digestive tract with blood, blood pumps
throw the aorta (A = 0.8 cm2) at a rate of 40 cm/s.
a. If all of the blood from the aorta travels into 2,400
arteries (area of each artery is 0.002 cm2), how fast is
the linear velocity of blood in a single artery?
b. Blood moves from the arteries to a billion capillaries,
which have a diameter of 8*10-4 cm. Assuming all blood
stays in the capillaries, what is the linear velocity of
blood in a single capillary?
c. How long does it take for 1 m3 of blood to flow through
the dog’s body, assuming continuity?