Air (1.23 kg/m³) flows past an object in a 2-m-diameter pipe and exits as a free jet as shown in the figure below. The velocity and pressure upstream are uniform at V = 16 m/s and p = 42 N/m², respectively. At the pipe exit the velocity is non-uniform as indicated. The shear stress along the pipe wall is negligible. (a) Determine the head loss associated with a fluid streamline as it flows over a solid body from the upstream region of uniform velocity to the wake region at the exit plane of the pipe. (b) Determine the force that the air puts on the object. Assume V₁ = 20.0 m/s, V₂ = 4 m/s. 2-m-dia. Air Wake 1-m dia. Exit- V₂ Head loss is associated with changes in static pressure head, dynamic pressure head, elevation and mechanical head in a flow.
Air (1.23 kg/m³) flows past an object in a 2-m-diameter pipe and exits as a free jet as shown in the figure below. The velocity and pressure upstream are uniform at V = 16 m/s and p = 42 N/m², respectively. At the pipe exit the velocity is non-uniform as indicated. The shear stress along the pipe wall is negligible. (a) Determine the head loss associated with a fluid streamline as it flows over a solid body from the upstream region of uniform velocity to the wake region at the exit plane of the pipe. (b) Determine the force that the air puts on the object. Assume V₁ = 20.0 m/s, V₂ = 4 m/s. 2-m-dia. Air Wake 1-m dia. Exit- V₂ Head loss is associated with changes in static pressure head, dynamic pressure head, elevation and mechanical head in a flow.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![Air (1.23 kg/m³) flows past an object in a 2-m-diameter pipe and exits as a free jet as shown in the figure below. The velocity and pressure upstream are uniform at \( V = 16 \, \text{m/s} \) and \( p = 42 \, \text{N/m}^2 \), respectively. At the pipe exit the velocity is non-uniform as indicated. The shear stress along the pipe wall is negligible.
(a) Determine the head loss associated with a fluid streamline as it flows over a solid body from the upstream region of uniform velocity to the wake region at the exit plane of the pipe.
(b) Determine the force that the air puts on the object. Assume \( V_1 = 20.0 \, \text{m/s} \), \( V_2 = 4.0 \, \text{m/s} \).
Diagram Explanation:
- The diagram shows a pipe with a diameter of 2 meters, with an object inside that creates a wake.
- The air flows from the left (upstream) to the right (exit), and the region is labeled with points indicating directions \( V_1 \) and \( V_2 \).
- The wake is 1-meter in diameter.
Questions:
- Head loss is associated with changes in static pressure head, dynamic pressure head, elevation, and mechanical head in a flow.
(a) Does the total head increase or decrease as it flows over the body? [Dropdown: Decrease]
(b) What is the decrease in pressure head from a location upstream of the object to a location at the exit plane in the wake of the object? \( \Delta P = \_\_\_ \, \text{m} \)
(c) What is the dynamic pressure head upstream of the object? \( P_d = \_\_\_ \)
(d) What is the dynamic pressure head of the fluid streamline in the wake region downstream of the object? \( P_w = \_\_\_ \)
(e) What is the decrease in dynamic pressure head from a location upstream of the object to a location at the exit plane in the wake of the object? \( \Delta P_{\text{dyn}} = \_\_\_ \)
(f) What is the change in elevation from a location upstream of the object to a location at the exit plane in the wake of the object? \( \Delta z = \_\_\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb3b63b4-702e-4c2c-936a-1674e5e2ea60%2F06acd75d-0342-4771-9bd1-efbc501299c8%2Fssm1a8e_processed.png&w=3840&q=75)
Transcribed Image Text:Air (1.23 kg/m³) flows past an object in a 2-m-diameter pipe and exits as a free jet as shown in the figure below. The velocity and pressure upstream are uniform at \( V = 16 \, \text{m/s} \) and \( p = 42 \, \text{N/m}^2 \), respectively. At the pipe exit the velocity is non-uniform as indicated. The shear stress along the pipe wall is negligible.
(a) Determine the head loss associated with a fluid streamline as it flows over a solid body from the upstream region of uniform velocity to the wake region at the exit plane of the pipe.
(b) Determine the force that the air puts on the object. Assume \( V_1 = 20.0 \, \text{m/s} \), \( V_2 = 4.0 \, \text{m/s} \).
Diagram Explanation:
- The diagram shows a pipe with a diameter of 2 meters, with an object inside that creates a wake.
- The air flows from the left (upstream) to the right (exit), and the region is labeled with points indicating directions \( V_1 \) and \( V_2 \).
- The wake is 1-meter in diameter.
Questions:
- Head loss is associated with changes in static pressure head, dynamic pressure head, elevation, and mechanical head in a flow.
(a) Does the total head increase or decrease as it flows over the body? [Dropdown: Decrease]
(b) What is the decrease in pressure head from a location upstream of the object to a location at the exit plane in the wake of the object? \( \Delta P = \_\_\_ \, \text{m} \)
(c) What is the dynamic pressure head upstream of the object? \( P_d = \_\_\_ \)
(d) What is the dynamic pressure head of the fluid streamline in the wake region downstream of the object? \( P_w = \_\_\_ \)
(e) What is the decrease in dynamic pressure head from a location upstream of the object to a location at the exit plane in the wake of the object? \( \Delta P_{\text{dyn}} = \_\_\_ \)
(f) What is the change in elevation from a location upstream of the object to a location at the exit plane in the wake of the object? \( \Delta z = \_\_\
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