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0. Math Review31m
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1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
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5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
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10. Conservation of Energy2h 54m
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14. Torque & Rotational Dynamics2h 5m
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18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
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21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
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24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
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31. Alternating Current2h 37m
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33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

19. Fluid Mechanics

Pressure Gauge: U-shaped Tube

Physics

19. Fluid Mechanics

Pressure Gauge: U-shaped Tube

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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 $7 . 9 cm .$ If the fluid level on the left is lower than on the right by a distance of $1 . 4 cm,$ what fluid was poured into the left side?

Gasoline

Ethyl alcohol

Water

Seawater

Glycerin

Blood (whole)

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Verified step by step guidance

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.