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Water flows at a rate of 2.4 ft3/s in an old, rusty 7.8-in.-diameter pipe that has a relative roughness of 0.010. It is proposed that by inserting a smooth plastic liner with an inside diameter of 7.0 in. into the old pipe as shown in the Figure the pressure drop per mile can be reduced. Is it true that the lined pipe can carry the required 2.4 ft3/s at a lower pressure drop than in the old pipe? Support your answer with appropriate calculations. 7.8in. Old Pressure drop is a function of flow rate and roughness. What is the mean velocity for the current 7.8 in. diameter pipe? V₂= 7.23 ft/s What is the Reynolds number for the current 7.8 in diameter pipe? Re- 388528 What is the friction factor for the current 7.8 in diameter pipe? fo-0.038 What is the pressure drop per mile for the current 7.8 in diameter pipe? Apo=4279.4 psi/mile -Liner 7.0in. New

Water flows at a rate of 2.4 ft3/s in an old, rusty 7.8-in.-diameter pipe that has a relative roughness of 0.010. It is proposed that by inserting a smooth plastic liner with an inside diameter of 7.0 in. into the old pipe as shown in the Figure the pressure drop per mile can be reduced. Is it true that the lined pipe can carry the required 2.4 ft3/s at a lower pressure drop than in the old pipe? Support your answer with appropriate calculations. 7.8in. Old Pressure drop is a function of flow rate and roughness. What is the mean velocity for the current 7.8 in. diameter pipe? V₂= 7.23 ft/s What is the Reynolds number for the current 7.8 in diameter pipe? Re- 388528 What is the friction factor for the current 7.8 in diameter pipe? fo-0.038 What is the pressure drop per mile for the current 7.8 in diameter pipe? Apo=4279.4 psi/mile -Liner 7.0in. New

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**Problem Context:** Water flows at a rate of 2.4 cubic feet per second (ft³/s) in an old, rusty pipe with a diameter of 7.8 inches and a relative roughness of 0.010. A proposal suggests inserting a smooth plastic liner with an inside diameter of 7.0 inches to reduce the pressure drop per mile. The task is to determine whether the lined pipe can maintain the flow rate of 2.4 ft³/s with a lower pressure drop than the old pipe, using appropriate calculations. **Diagrams:** - Two diagrams represent the pipes: 1. **Old Pipe:** Diameter = 7.8 inches 2. **New Lined Pipe:** Diameter = 7.0 inches **Calculations:** 1. **Mean Velocity for the 7.8-inch Diameter Pipe:** - \( V_o = 7.23 \, \text{ft/s} \) 2. **Reynolds Number for the 7.8-inch Diameter Pipe:** - \( \text{Re} = 388528 \) 3. **Friction Factor for the 7.8-inch Diameter Pipe:** - \( f_o = 0.038 \) 4. **Pressure Drop per Mile for the 7.8-inch Diameter Pipe:** - \( \Delta P_o = 4279.4 \, \text{psi/mile} \) **Conclusion:** The problem explores whether the lined pipe can achieve a lower pressure drop at the given flow rate, requiring further calculations for the new lined pipe and comparison with the old pipe's pressure drop.
Transcribed Image Text:**Problem Context:** Water flows at a rate of 2.4 cubic feet per second (ft³/s) in an old, rusty pipe with a diameter of 7.8 inches and a relative roughness of 0.010. A proposal suggests inserting a smooth plastic liner with an inside diameter of 7.0 inches to reduce the pressure drop per mile. The task is to determine whether the lined pipe can maintain the flow rate of 2.4 ft³/s with a lower pressure drop than the old pipe, using appropriate calculations. **Diagrams:** - Two diagrams represent the pipes: 1. **Old Pipe:** Diameter = 7.8 inches 2. **New Lined Pipe:** Diameter = 7.0 inches **Calculations:** 1. **Mean Velocity for the 7.8-inch Diameter Pipe:** - \( V_o = 7.23 \, \text{ft/s} \) 2. **Reynolds Number for the 7.8-inch Diameter Pipe:** - \( \text{Re} = 388528 \) 3. **Friction Factor for the 7.8-inch Diameter Pipe:** - \( f_o = 0.038 \) 4. **Pressure Drop per Mile for the 7.8-inch Diameter Pipe:** - \( \Delta P_o = 4279.4 \, \text{psi/mile} \) **Conclusion:** The problem explores whether the lined pipe can achieve a lower pressure drop at the given flow rate, requiring further calculations for the new lined pipe and comparison with the old pipe's pressure drop.
**Understanding Pressure Drop in Pipes: Key Parameters** Pressure drop in a pipe system is influenced by both flow rate and the roughness of the pipe. Here we examine critical parameters for a 7.0-inch diameter pipe. - **Mean Velocity (Vo):** The average flow velocity in the pipe is given as **8.93 feet per second (ft/s)**. This value is crucial for calculating other parameters like Reynolds number and pressure drop. - **Reynolds Number (Re):** The Reynolds number, an important dimensionless quantity in fluid mechanics, describes the flow regime. For the new 7.0-inch diameter pipe, the Reynolds number is **539717.5**. High Reynolds numbers indicate turbulent flow, which influences pressure drop and friction factor. - **Friction Factor (fo):** The friction factor, denoted as **0.0116**, is a dimensionless number used to calculate the pressure drop due to pipe friction. It's a function of the pipe's roughness and flow conditions. - **Pressure Drop (ΔPo):** The pressure drop per mile for the 7.0-inch diameter pipe is **20.75 psi/mile**. This value is critical for designing efficient piping systems to ensure adequate pressure maintenance throughout. These parameters help in understanding fluid dynamics in pipes and optimizing system design for efficient fluid transport.
Transcribed Image Text:**Understanding Pressure Drop in Pipes: Key Parameters** Pressure drop in a pipe system is influenced by both flow rate and the roughness of the pipe. Here we examine critical parameters for a 7.0-inch diameter pipe. - **Mean Velocity (Vo):** The average flow velocity in the pipe is given as **8.93 feet per second (ft/s)**. This value is crucial for calculating other parameters like Reynolds number and pressure drop. - **Reynolds Number (Re):** The Reynolds number, an important dimensionless quantity in fluid mechanics, describes the flow regime. For the new 7.0-inch diameter pipe, the Reynolds number is **539717.5**. High Reynolds numbers indicate turbulent flow, which influences pressure drop and friction factor. - **Friction Factor (fo):** The friction factor, denoted as **0.0116**, is a dimensionless number used to calculate the pressure drop due to pipe friction. It's a function of the pipe's roughness and flow conditions. - **Pressure Drop (ΔPo):** The pressure drop per mile for the 7.0-inch diameter pipe is **20.75 psi/mile**. This value is critical for designing efficient piping systems to ensure adequate pressure maintenance throughout. These parameters help in understanding fluid dynamics in pipes and optimizing system design for efficient fluid transport.
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