4.0 mm Consider the following diagram. (let air be an ideal, incompressible fluid) 2.0 cm 1200 cm's a. If the air is found to have a flow rate of 1200 cm³/s as it leaves the Hg 4.00 mm diameter pipe, what is the velocity of the air in both segments of the pipe? p. If the density of air is 1.28 kg/m³ and the end of the pipe on the right opens up to the atmosphere, what is the pressure of the pipe at the 2.00 cm diameter section?

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**Problem Description:**

Consider the following diagram. (Let air be an ideal, incompressible fluid)

**Diagram Summary:**

The diagram shows a pipe system with two sections of different diameters and a U-tube containing mercury. The pipe transitions from a 4.00 mm diameter section to a 2.00 cm diameter section. Air flows through the pipe and mercury occupies the bottom of the U-tube.

**Questions:**

a. If the air is found to have a flow rate of 1200 cm³/s as it leaves the 4.00 mm diameter pipe, what is the velocity of the air in both segments of the pipe?

b. If the density of air is 1.28 kg/m³ and the end of the pipe on the right opens up to the atmosphere, what is the pressure of the pipe at the 2.00 cm diameter section?

c. If the fluid in the bottom of the U-tube is mercury with a density of 13,600 kg/m³ what is the difference between the surface levels of both sides of the tube, marked as h in the diagram?

**Diagram Explanation:**

- **Pipe System:** The diagram highlights a transition between a narrow 4.00 mm diameter section and a wider 2.00 cm diameter section through which air flows with a specific volume rate.
- **U-Tube:** Displays mercury in the bottom and open sections marked to denote the different liquid levels, which are to be compared to find the height difference \( h \).

These components describe a typical fluid dynamics scenario analyzing flow rates, velocities, pressure differences, and static fluid balance.
Transcribed Image Text:**Problem Description:** Consider the following diagram. (Let air be an ideal, incompressible fluid) **Diagram Summary:** The diagram shows a pipe system with two sections of different diameters and a U-tube containing mercury. The pipe transitions from a 4.00 mm diameter section to a 2.00 cm diameter section. Air flows through the pipe and mercury occupies the bottom of the U-tube. **Questions:** a. If the air is found to have a flow rate of 1200 cm³/s as it leaves the 4.00 mm diameter pipe, what is the velocity of the air in both segments of the pipe? b. If the density of air is 1.28 kg/m³ and the end of the pipe on the right opens up to the atmosphere, what is the pressure of the pipe at the 2.00 cm diameter section? c. If the fluid in the bottom of the U-tube is mercury with a density of 13,600 kg/m³ what is the difference between the surface levels of both sides of the tube, marked as h in the diagram? **Diagram Explanation:** - **Pipe System:** The diagram highlights a transition between a narrow 4.00 mm diameter section and a wider 2.00 cm diameter section through which air flows with a specific volume rate. - **U-Tube:** Displays mercury in the bottom and open sections marked to denote the different liquid levels, which are to be compared to find the height difference \( h \). These components describe a typical fluid dynamics scenario analyzing flow rates, velocities, pressure differences, and static fluid balance.
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