Fluid mechanics problem ### Example Problem P3.180: Flow System AnalysisIn the figure provided, we observe a simplified model of a fluid flow system involving a pump. This system consists of two reservoirs with distinct elevations and a connecting pipeline incorporating a pump. #### Key Components:1. **Reservoirs:** - **Reservoir 1 (on the right)** - **Elevation (z1):** 50 feet above the reference level. - **Reservoir 2 (on the left)** - **Elevation (z2):** 150 feet above the reference level.2. **Connecting Pipeline:** - The pipeline diameter (D) is 6 inches.3. **Pump:** - Located at the base of the system, the pump is responsible for moving the fluid from Reservoir 1 to Reservoir 2 against the elevation difference.#### System Functionality:The system’s primary function is to transport fluid from the lower elevation (50 feet) in Reservoir 1 to the higher elevation (150 feet) in Reservoir 2. This is accomplished by the pump, which imparts energy to the fluid, enabling it to overcome the gravitational potential energy difference between the two reservoirs.Blue arrows in the diagram indicate the direction of fluid flow, starting from Reservoir 1, passing through the pump, and finally reaching Reservoir 2.### Detailed Explanation of the Diagram- **Elevations (z1 and z2):** The elevations are labeled next to each reservoir, providing a clear reference for the height difference the pump must overcome.- **Flow Direction:** The flow direction is denoted by blue arrows, which guide the observer from the point of fluid intake at Reservoir 1, through the pump, and to the discharge at Reservoir 2.- **Pump Location:** The pump, represented in the central part of the pipeline, is depicted to highlight its key role in the system.Understanding the mechanics of such systems is crucial in various fields of engineering, including civil, environmental, and mechanical engineering. The elevation differences and the properties of the pump are essential details for calculating the energy requirements, flow rates, and pressure drops in fluid dynamics problems.This diagram serves as an educational tool for visualizing the interaction between different system components and for analyzing fluid movement within a complex system. ### Pump Horsepower CalculationWater at 20°C is pumped at a rate of 1500 gallons per minute (gal/min) from the lower to the upper reservoir, as shown in Figure P3.180. Pipe friction losses are approximated by the equation:\[ h_f \approx \frac{27V^2}{2g} \]where:- \( h_f \) = friction loss- \( V \) = average velocity in the pipe- \( g \) = acceleration due to gravity (9.81 m/s²)The pump operates with an efficiency of 75 percent (0.75). The goal is to determine the horsepower needed to drive the pump under these conditions. ### Steps to Solve:1. **Determine the Flow Rate**: - Given flow rate = 1500 gal/min2. **Conversion of Flow Rate**: - Convert gallons per minute to cubic feet per second (cfs), for more consistent units in calculations.3. **Calculate Velocity**: - Find the average velocity (V) in the pipe by considering the cross-sectional area of the pipe and the flow rate.4. **Calculate Friction Loss**: - Using the given formula for \( h_f \), plug in the values to determine the friction losses.5. **Calculate Power Requirement**: - Total power (Watts or Horsepower) required taking into account the efficiency of the pump. - Adjust for the given efficiency to find the actual horsepower needed.### Final Calculation1. \( V \) must be computed based on the specific details of the pipe's dimensions.2. \( h_f \) is then calculated with the value of \( V \).3. Power required can be calculated, considering energy losses due to friction and head height.4. Adjust the power calculated for efficiency (divide by 0.75).Note: Figure P3.180 mentioned in the text likely shows the setup of the reservoirs and pipes which is necessary to understand the height difference and details for calculating total head. As the figure is not provided here, the exact numerical solution would need these additional details. ---This guiding text would help students understand the steps needed to solve for the required horsepower to drive a pump that moves water from one reservoir to another, considering efficiency and friction losses. Understanding these fundamentals is key to solving fluid dynamics problems in an educational context.

Write the expression of the velocity of water in the pipe. Write the expression of the frictional…

Water at 20°C is pumped at 1500 gal/min from the lower to upper reservoir, as in Fig. P3.180. Pipe friction losses are approximated by h,~ 27V²/(2g), where Vis the average velocity in the pipe. If the pump is 75 percent efficient, what horsepower is needed to drive it? the

Water at 20°C is pumped at 1500 gal/min from the lower to upper reservoir, as in Fig. P3.180. Pipe friction losses are approximated by h,~ 27V²/(2g), where Vis the average velocity in the pipe. If the pump is 75 percent efficient, what horsepower is needed to drive it? the

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

Fluid mechanics problem

### Example Problem P3.180: Flow System Analysis

In the figure provided, we observe a simplified model of a fluid flow system involving a pump. This system consists of two reservoirs with distinct elevations and a connecting pipeline incorporating a pump.

#### Key Components:
1. **Reservoirs:**
- **Reservoir 1 (on the right)**
- **Elevation (z1):** 50 feet above the reference level.
- **Reservoir 2 (on the left)**
- **Elevation (z2):** 150 feet above the reference level.

2. **Connecting Pipeline:**
- The pipeline diameter (D) is 6 inches.

3. **Pump:**
- Located at the base of the system, the pump is responsible for moving the fluid from Reservoir 1 to Reservoir 2 against the elevation difference.

#### System Functionality:
The system’s primary function is to transport fluid from the lower elevation (50 feet) in Reservoir 1 to the higher elevation (150 feet) in Reservoir 2. This is accomplished by the pump, which imparts energy to the fluid, enabling it to overcome the gravitational potential energy difference between the two reservoirs.

Blue arrows in the diagram indicate the direction of fluid flow, starting from Reservoir 1, passing through the pump, and finally reaching Reservoir 2.

### Detailed Explanation of the Diagram
- **Elevations (z1 and z2):** The elevations are labeled next to each reservoir, providing a clear reference for the height difference the pump must overcome.
- **Flow Direction:** The flow direction is denoted by blue arrows, which guide the observer from the point of fluid intake at Reservoir 1, through the pump, and to the discharge at Reservoir 2.
- **Pump Location:** The pump, represented in the central part of the pipeline, is depicted to highlight its key role in the system.

Understanding the mechanics of such systems is crucial in various fields of engineering, including civil, environmental, and mechanical engineering. The elevation differences and the properties of the pump are essential details for calculating the energy requirements, flow rates, and pressure drops in fluid dynamics problems.

This diagram serves as an educational tool for visualizing the interaction between different system components and for analyzing fluid movement within a complex system.

### Pump Horsepower Calculation

Water at 20°C is pumped at a rate of 1500 gallons per minute (gal/min) from the lower to the upper reservoir, as shown in Figure P3.180.

Pipe friction losses are approximated by the equation:
\[ h_f \approx \frac{27V^2}{2g} \]
where:
- \( h_f \) = friction loss
- \( V \) = average velocity in the pipe
- \( g \) = acceleration due to gravity (9.81 m/s²)

The pump operates with an efficiency of 75 percent (0.75). The goal is to determine the horsepower needed to drive the pump under these conditions.

### Steps to Solve:

1. **Determine the Flow Rate**:
- Given flow rate = 1500 gal/min

2. **Conversion of Flow Rate**:
- Convert gallons per minute to cubic feet per second (cfs), for more consistent units in calculations.

3. **Calculate Velocity**:
- Find the average velocity (V) in the pipe by considering the cross-sectional area of the pipe and the flow rate.

4. **Calculate Friction Loss**:
- Using the given formula for \( h_f \), plug in the values to determine the friction losses.

5. **Calculate Power Requirement**:
- Total power (Watts or Horsepower) required taking into account the efficiency of the pump.
- Adjust for the given efficiency to find the actual horsepower needed.

### Final Calculation
1. \( V \) must be computed based on the specific details of the pipe's dimensions.
2. \( h_f \) is then calculated with the value of \( V \).
3. Power required can be calculated, considering energy losses due to friction and head height.
4. Adjust the power calculated for efficiency (divide by 0.75).

Note: Figure P3.180 mentioned in the text likely shows the setup of the reservoirs and pipes which is necessary to understand the height difference and details for calculating total head. As the figure is not provided here, the exact numerical solution would need these additional details.

---

This guiding text would help students understand the steps needed to solve for the required horsepower to drive a pump that moves water from one reservoir to another, considering efficiency and friction losses. Understanding these fundamentals is key to solving fluid dynamics problems in an educational context.

Branch of science that deals with the stationary and moving bodies under the influence of forces.

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