A stainless steel tank contains 2% fat milk (SG = 1.030). A pressure gauge at th

Question

A stainless steel tank contains 2% fat milk (SG = 1.030). A pressure gauge at the bottom of the tank monitors the gauge pressure of the vessel, and from that reading, the height of milk within the tank can be determined. Which plot best describes the relationship between the height of the milk and the gauge pressure? What height of milk would give a gauge pressure of 41.0 kPa? If the tank was actually pressurized such that the top surface of the milk was at a pressure of 116.0 kPa, what was the actual height of milk in the tank? If the tank was pressurized above atmospheric pressure, then the gauge will read a pressure higher than the pressure contributed by just the height of the milk in the tank. To find the actual height in the tank, subtract the difference between the top surface pressure and the atmospheric pressure from the gauge pressure. Set this new pressure equal to the hydrostatic pressure and solve for h.

Explanation / Answer

1) we know that

Pgauge = h x d x g

where

h = ( 1 / d x g) Pgauge

comparing with y = mx

it is a straight line passing through the origin

so

the plot is A

2)

we know that

specific gravity = density of subtance / density of water

so

1.03 = density of milk / 1000

density of milk = 1030 kg / m3

now

Pgauge = h x d x g

given

Pgauge = 41 x 1000 Pa

so

41 x 1000 = h x 1030 x 9.8

h = 4.06

so

the height is 4.06 m

3)

now

consider a pressure Ptop

so

the new equation is

Pg - (Ptop - Patm) = h x d x g

so

41000 - ( 116000 - 101325) = h x 1030 x 9.8

h = 2.608

so

the actual height of milk in the tank is 2.608 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.