A liquid of density 1230 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.47 m/s and the pipe diameter ?1 is 11.3 cm. At Location 2, the pipe diameter ?2 is 14.5 cm. At Location 1, the pipe is Δ?=8.69 m higher than it is at Location 2. Ignoring viscosity, calculate the difference Δ? between the fluid pressure at Location 2 and the fluid pressure at Location 1.
A liquid of density 1230 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.47 m/s and the pipe diameter ?1 is 11.3 cm. At Location 2, the pipe diameter ?2 is 14.5 cm. At Location 1, the pipe is Δ?=8.69 m higher than it is at Location 2. Ignoring viscosity, calculate the difference Δ? between the fluid pressure at Location 2 and the fluid pressure at Location 1.
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A liquid of density 1230 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.47 m/s and the pipe diameter ?1 is 11.3 cm. At Location 2, the pipe diameter ?2 is 14.5 cm. At Location 1, the pipe is Δ?=8.69 m higher than it is at Location 2. Ignoring viscosity, calculate the difference Δ? between the fluid pressure at Location 2 and the fluid pressure at Location 1.
![### Understanding Fluid Dynamics: A Simple Pipe System
#### Diagram Description
The diagram presented illustrates a pipe system with two distinct locations, labeled Location 1 and Location 2.
1. **Pipe Structure:**
- The pipe has a bend forming an 'S' shape.
- From Location 1, the pipe descends vertically, then bends horizontally to the right, and then vertically downward again to Location 2.
2. **Dimensions:**
- The diameter at Location 1 is denoted by \( d_1 \).
- The diameter at Location 2 is denoted by \( d_2 \).
- The vertical distance between Location 1 and Location 2 is represented by \( \Delta y \).
### Analysis in Fluid Dynamics
This diagram is useful in the study of fluid dynamics as it helps to understand various concepts such as pressure changes, velocity, and Bernoulli’s principle within a pipe system. Here’s a breakdown of what the parameters may represent and their importance:
- **\( d_1 \) and \( d_2 \):**
The diameters of the pipe at the two locations affect the velocity of the fluid passing through. According to the principle of continuity for steady flow, the product of the cross-sectional area and velocity remains constant along the pipe. This can be represented as:
\[
A_1V_1 = A_2V_2
\]
Where \( A \) is the cross-sectional area and \( V \) is the fluid velocity.
- **\( \Delta y \):**
The vertical distance (\( \Delta y \)) between the two locations affects the pressure difference due to gravitational force, which may need to be considered in applications of Bernoulli’s equation:
\[
P_1 + \frac{1}{2}\rho V_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho V_2^2 + \rho g h_2
\]
Where \( P \) is pressure, \( \rho \) is fluid density, \( g \) is acceleration due to gravity, \( h \) is the height, and \( V \) is the velocity of the fluid at different locations.
### Practical Applications
Understanding the flow dynamics within such a pipe system is crucial in various engineering and physics applications, such as:
- **Water Distribution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba74a81d-a4a4-4b2b-9546-a0067c022a51%2F5ca56a19-df06-4969-bd3f-74ac9e5796fb%2F7rmx65.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Fluid Dynamics: A Simple Pipe System
#### Diagram Description
The diagram presented illustrates a pipe system with two distinct locations, labeled Location 1 and Location 2.
1. **Pipe Structure:**
- The pipe has a bend forming an 'S' shape.
- From Location 1, the pipe descends vertically, then bends horizontally to the right, and then vertically downward again to Location 2.
2. **Dimensions:**
- The diameter at Location 1 is denoted by \( d_1 \).
- The diameter at Location 2 is denoted by \( d_2 \).
- The vertical distance between Location 1 and Location 2 is represented by \( \Delta y \).
### Analysis in Fluid Dynamics
This diagram is useful in the study of fluid dynamics as it helps to understand various concepts such as pressure changes, velocity, and Bernoulli’s principle within a pipe system. Here’s a breakdown of what the parameters may represent and their importance:
- **\( d_1 \) and \( d_2 \):**
The diameters of the pipe at the two locations affect the velocity of the fluid passing through. According to the principle of continuity for steady flow, the product of the cross-sectional area and velocity remains constant along the pipe. This can be represented as:
\[
A_1V_1 = A_2V_2
\]
Where \( A \) is the cross-sectional area and \( V \) is the fluid velocity.
- **\( \Delta y \):**
The vertical distance (\( \Delta y \)) between the two locations affects the pressure difference due to gravitational force, which may need to be considered in applications of Bernoulli’s equation:
\[
P_1 + \frac{1}{2}\rho V_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho V_2^2 + \rho g h_2
\]
Where \( P \) is pressure, \( \rho \) is fluid density, \( g \) is acceleration due to gravity, \( h \) is the height, and \( V \) is the velocity of the fluid at different locations.
### Practical Applications
Understanding the flow dynamics within such a pipe system is crucial in various engineering and physics applications, such as:
- **Water Distribution
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