A U-tube open at both ends is partially filled with water (Figure (a)). Oil (? = 750 kg/m3) is then poured into the right arm and forms a column L = 5.34 cm high (Figure (b)). (a) Determine the difference h in the heights of the two liquid surfaces. (The density of water is 1.00 ✕ 103 kg/m3.) (b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Figure (c)). Determine the speed of the air being blown across the left arm. Assume the density of air is 1.29 kg/m3.
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
A U-tube open at both ends is partially filled with water (Figure (a)). Oil (? = 750 kg/m3) is then poured into the right arm and forms a column L = 5.34 cm high (Figure (b)).
(a) Determine the difference h in the heights of the two liquid surfaces. (The density of water is 1.00 ✕ 103 kg/m3.)
(b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Figure (c)). Determine the speed of the air being blown across the left arm. Assume the density of air is 1.29 kg/m3.
![The image illustrates a sequence of three diagrams (a, b, and c) depicting fluid dynamics and pressure in a U-tube.
**Diagram (a):**
- A U-tube is filled with water, represented by a blue liquid.
- The open ends of the tube are exposed to atmospheric pressure, denoted as \( P_0 \).
**Diagram (b):**
- The U-tube now contains two immiscible liquids: water at the bottom and oil (depicted as a lighter-colored liquid) sitting on top of the water in the right arm of the U-tube.
- The height of the oil column is marked as \( L \), while the height difference between the water levels in each arm is denoted by \( h \).
**Diagram (c):**
- Similar to diagram (b), with oil above water in the right arm.
- An arrow labeled \(\vec{v}\) points towards the top of the oil column, indicating motion or force applied in that direction.
- A "Shield" is placed above the oil, suggesting an interaction or protection against external factors.
- The height \( L \) of the oil column remains noted.
These diagrams illustrate principles such as fluid pressure, buoyancy, and the behavior of immiscible liquids in a U-tube when subject to external forces or pressure differences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1609891-a095-464f-bd32-ff9f26049048%2Faf8a33c0-5a43-49a3-a7b8-a0713bcb02cc%2Fs05zhtd_processed.png&w=3840&q=75)
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