Multiple Choice
Water and oil are poured into a u-shape tube, as shown below. The column of oil, on the right side, is 25 cm tall, and the distance between the top of the two columns is 9 cm. Calculate the density of the oil.
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19. Fluid Mechanics
Pressure Gauge: U-shaped Tube
Multiple Choice
A U-shaped tube open at both ends is initially partly filled with oil. Then a different liquid is poured into the left side. The height of the column of mystery fluid is If the fluid level on the left is lower than on the right by a distance of what fluid was poured into the left side?
A
Gasoline
B
Ethyl alcohol
C
Water
D
Seawater
E
Glycerin
F
Blood (whole)
Verified step by step guidance1
Understand that the problem involves a U-shaped tube with two different fluids, and we need to determine the identity of the mystery fluid based on the height difference in the fluid levels.
Apply the principle of hydrostatic pressure, which states that the pressure at the same horizontal level in a fluid at rest is the same. This means the pressure exerted by the column of mystery fluid on the left must equal the pressure exerted by the column of oil on the right.
Set up the equation for hydrostatic pressure: \( \rho_{mystery} \cdot g \cdot h_{mystery} = \rho_{oil} \cdot g \cdot h_{oil} \), where \( \rho \) is the density, \( g \) is the acceleration due to gravity, and \( h \) is the height of the fluid column.
Given that the height of the mystery fluid column is 7.9 cm and the height difference is 1.4 cm, calculate the effective height of the oil column as \( h_{oil} = h_{mystery} + 1.4 \text{ cm} \).
Use the known densities of the potential fluids (Gasoline, Ethyl alcohol, Water, Seawater, Glycerin, and Blood) to solve the equation for \( \rho_{mystery} \) and determine which fluid matches the calculated density.
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