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Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3?
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Using bernoulli equation , in a Smooth pipe of uniform diameter 120 c...
**Bernoulli's Equation and Its Application**
Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and height of a fluid flowing in a pipe. It is based on the conservation of energy principle and is used to analyze the flow of fluids through pipes or channels.
**Given Data**
- Diameter of the pipe: 120 cm = 1.2 m
- Pressure at section A: 50 kPa
- Elevation at section A: 20 m
- Pressure at section B: 30 kPa
- Elevation at section B: 15 m
- Flow rate through the pipe: 12 m^3/sec
- Density of water: 1000 kg/m^3
**Determining the Flow Direction**
To determine the flow direction between section A and section B, we need to compare the pressures at these two sections. According to Bernoulli's equation, the flow will be from a region of higher pressure to a region of lower pressure. In this case, the pressure at section A is 50 kPa, while the pressure at section B is 30 kPa. Therefore, the flow will be from section A to section B.
**Calculating the Total Head Loss**
The total head loss in the pipe can be determined using Bernoulli's equation. The equation can be written as:
P1/ρg + V1^2/2g + h1 = P2/ρg + V2^2/2g + h2
Where:
P1 and P2 are the pressures at sections A and B, respectively.
ρ is the density of the fluid (water in this case).
g is the acceleration due to gravity.
V1 and V2 are the velocities at sections A and B, respectively.
h1 and h2 are the elevations at sections A and B, respectively.
**Applying Bernoulli's Equation**
Using the given data, we can apply Bernoulli's equation to find the total head loss.
P1/ρg + V1^2/2g + h1 = P2/ρg + V2^2/2g + h2
Substituting the values:
(50,000 Pa)/(1000 kg/m^3 * 9.8 m/s^2) + 0 + 20 m = (30,000 Pa)/(1000 kg/m^3 * 9.8 m/s^2) + 0 + 15 m
Simplifying the equation:
50/9.8 + 20 = 30/9.8 + 15
Calculating the values:
5.102 + 20 = 3.061 + 15
25.102 = 18.061
Therefore, the total head loss in the pipe is 25.102 meters.
**Conclusion**
Based on Bernoulli's equation, the flow direction between section A and section B is from A to B. The total head loss in the pipe is calculated to be 25.102 meters. This analysis helps us understand the flow behavior and pressure distribution in the pipe, which is crucial for designing and analyzing fluid systems.
Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and height of a fluid flowing in a pipe. It is based on the conservation of energy principle and is used to analyze the flow of fluids through pipes or channels.
**Given Data**
- Diameter of the pipe: 120 cm = 1.2 m
- Pressure at section A: 50 kPa
- Elevation at section A: 20 m
- Pressure at section B: 30 kPa
- Elevation at section B: 15 m
- Flow rate through the pipe: 12 m^3/sec
- Density of water: 1000 kg/m^3
**Determining the Flow Direction**
To determine the flow direction between section A and section B, we need to compare the pressures at these two sections. According to Bernoulli's equation, the flow will be from a region of higher pressure to a region of lower pressure. In this case, the pressure at section A is 50 kPa, while the pressure at section B is 30 kPa. Therefore, the flow will be from section A to section B.
**Calculating the Total Head Loss**
The total head loss in the pipe can be determined using Bernoulli's equation. The equation can be written as:
P1/ρg + V1^2/2g + h1 = P2/ρg + V2^2/2g + h2
Where:
P1 and P2 are the pressures at sections A and B, respectively.
ρ is the density of the fluid (water in this case).
g is the acceleration due to gravity.
V1 and V2 are the velocities at sections A and B, respectively.
h1 and h2 are the elevations at sections A and B, respectively.
**Applying Bernoulli's Equation**
Using the given data, we can apply Bernoulli's equation to find the total head loss.
P1/ρg + V1^2/2g + h1 = P2/ρg + V2^2/2g + h2
Substituting the values:
(50,000 Pa)/(1000 kg/m^3 * 9.8 m/s^2) + 0 + 20 m = (30,000 Pa)/(1000 kg/m^3 * 9.8 m/s^2) + 0 + 15 m
Simplifying the equation:
50/9.8 + 20 = 30/9.8 + 15
Calculating the values:
5.102 + 20 = 3.061 + 15
25.102 = 18.061
Therefore, the total head loss in the pipe is 25.102 meters.
**Conclusion**
Based on Bernoulli's equation, the flow direction between section A and section B is from A to B. The total head loss in the pipe is calculated to be 25.102 meters. This analysis helps us understand the flow behavior and pressure distribution in the pipe, which is crucial for designing and analyzing fluid systems.
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Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3?
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Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3?.
Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3?.
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Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3?, a detailed solution for Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3? has been provided alongside types of Using bernoulli equation , in a Smooth pipe of uniform diameter 120 cm, it is recorded that section A is having a pressure of 50kpa and height of 20m. the section B is having an elevation of 15m and its pressure was recorded as 30kpa. The flow rate through the pipe is 12m^3/sec. Determine the direction of flow between section A and B. What is the total head loss? Density of the water =1000kg/m3? theory, EduRev gives you an
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