### Problem StatementConsider the flow of oil with a density (\( \rho \)) of 870 kg/m\(^3\) and dynamic viscosity (\( \mu \)) of 1.03 kg/m·s in a pipeline. The pipeline has a diameter of 3 cm and a length of 1.5 m. The oil flows through the pipe with an average velocity of 4 m/s. #### Objectives1. Determine the pressure drop from one end of the pipe to the other.2. Calculate the volume flow rate.3. Compute the pumping power required to maintain the flow of oil.*Note: Neglect minor losses.*### ExplanationTo analyze this scenario, the following calculations might be performed:1. **Pressure Drop Calculation:** - Use the Darcy-Weisbach equation to determine the head loss due to friction, and then convert it to pressure drop.2. **Volume Flow Rate:** - Calculate using the formula \( Q = A \cdot V \), where \( Q \) is the volume flow rate, \( A \) is the cross-sectional area of the pipe, and \( V \) is the velocity.3. **Pumping Power:** - Calculate the power required to overcome the pressure drop, using the formula \( P = Q \cdot \Delta P \), where \( P \) is power, \( Q \) is the flow rate, and \( \Delta P \) is the pressure drop.

Given data: density, ρ=870 kg/m3 dynamic viscosity, μ=1.03 kg/m-s diameter, d = 3 m = 0.03 m diameter, d = 1.5 m average velocity, v =4 m/s Determine, 1. Pressure drop P1-P2 2. Volume flow rate( Q) 3. Pumping power (P) Hint: neglect the minor lossesWe know that the Darcy's formula The head lost (hf) due to friction can be determined by the following equation hf=fLv22gd m ----------------- 1 Determine the friction coefficient To find the f, calculate the Reynold's number Re=ρVDμ Where V = velocity of oil flowing in pipe D = diameter of pipe, m μ=viscosity of oil. ρ=density of oil, kg/m3 Substituting the values in the Reynold's number Re=870×4×0.031.03 Re=101.35 Conditions to calculate coefficient of friction based on Reynold's number 1. f=16Re for Re<2000 2. f=0.079Re1/4for 4000 to 106 Obtained Reynold's number is less than than 2000. Therefore, the first equation is valid for calculation of 'f' f=16101.35for Re<2000 f=0.1548 Now substitute the value of f in the equation 1hf=0.1548×1.5×422×9.81×0.03 m hf=6.312 m The head lost due to friction, neglecting the minor losses is 6.312 m 1. The pressure loss from one end to other end General equation of pressure P=ρgh Pa Between two points of a pipe P1-P2=ρghf Pa P1-P2=870 ×9.81×6.312 Pa P1-P2=53871.02 Pa P1-P2=53.871 kPa The pressure loss is 53.871 kPa. 2. The Volume flow rate (Q) Q=AV m3/sA=π4(0.03)2 = 0.007 m2 Q=AV m3/s Q=0.0007×4 m3/s Q=0.00282 m3/s=2.82×10-3 m3/s The volume flow rate is 2.82×10-3 m3/s 3. Pumping power (P) P=ρgQhf1000 kW P=870×9.81×2.82×10-3×6.3121000 kW P=0.152 kW P=152 W The pumping power is 152 kW.

Engineering

Mechanical Engineering

Consider the flow of oil with p = 870 kg/m² and u = 1.03 kg/m-s in a 3-cm-diameter, 1.5-m-long section, pipeline at an average velocity of 4 m/s. Determine the pressure drop from one end of the pipe to the other, the volume flow rate, and the pumping power required to maintain the flow of oil. Neglect minor losses.

Consider the flow of oil with p = 870 kg/m² and u = 1.03 kg/m-s in a 3-cm-diameter, 1.5-m-long section, pipeline at an average velocity of 4 m/s. Determine the pressure drop from one end of the pipe to the other, the volume flow rate, and the pumping power required to maintain the flow of oil. Neglect minor losses.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

### Problem Statement

Consider the flow of oil with a density (\( \rho \)) of 870 kg/m\(^3\) and dynamic viscosity (\( \mu \)) of 1.03 kg/m·s in a pipeline. The pipeline has a diameter of 3 cm and a length of 1.5 m. The oil flows through the pipe with an average velocity of 4 m/s.

#### Objectives

1. Determine the pressure drop from one end of the pipe to the other.
2. Calculate the volume flow rate.
3. Compute the pumping power required to maintain the flow of oil.

*Note: Neglect minor losses.*

### Explanation

To analyze this scenario, the following calculations might be performed:

1. **Pressure Drop Calculation:**
- Use the Darcy-Weisbach equation to determine the head loss due to friction, and then convert it to pressure drop.

2. **Volume Flow Rate:**
- Calculate using the formula \( Q = A \cdot V \), where \( Q \) is the volume flow rate, \( A \) is the cross-sectional area of the pipe, and \( V \) is the velocity.

3. **Pumping Power:**
- Calculate the power required to overcome the pressure drop, using the formula \( P = Q \cdot \Delta P \), where \( P \) is power, \( Q \) is the flow rate, and \( \Delta P \) is the pressure drop.

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