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Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column.
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Water is flowing through a horizontal tube 4 km in length and 4 cm in ...
Volume of the tube = pi r^2 L = pi * 4/100 * 4/100 * 4000 m^3
Volume of water flown per second = 20 ltr = 20 * 10^-3 m^3 /s
So time of flow = pi * 4/100 * 4/100 * 4000 / 20 * 10^-3
==> 320 pi second
So velocity of rush = 4000 / 320 pi = 25/2pi m/s
Hence kinetic energy of liquid going out 1/2 * ρ * V * v^2
Force = Pressure * area
Work performed to push water through length of tube = Pressure * area * length = pressure * volume = P * V
By the conservation of energy P V = 1/2 * ρ * V * v^2
Cancelling and plugging v you can get P = 125 * 625 / pi^2 Pa
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Water is flowing through a horizontal tube 4 km in length and 4 cm in ...
Calculation of Pressure Required to Maintain Flow in Terms of Height of Mercury Column
Given:
- Length of the tube = 4 km = 4000 m
- Radius of the tube = 4 cm = 0.04 m
- Rate of water flow = 20 liters/second
Step 1: Convert the given measurements
- Convert the length of the tube from kilometers to meters: 4 km = 4000 m
- Convert the radius of the tube from centimeters to meters: 4 cm = 0.04 m
Step 2: Calculate the cross-sectional area of the tube
- The cross-sectional area (A) of a tube can be calculated using the formula: A = πr^2, where r is the radius of the tube.
- Substituting the given values, A = π(0.04)^2 = 0.0016π m^2
Step 3: Calculate the volume of water flowing per second
- The volume of water flowing per second can be calculated using the formula: Volume = flow rate × time
- Substituting the given values, Volume = 20 liters/second = 0.02 m^3/second
Step 4: Calculate the velocity of water flow
- The velocity (v) of water flow can be calculated using the formula: v = Volume / A
- Substituting the calculated values, v = (0.02 m^3/second) / (0.0016π m^2) ≈ 3.98 m/second
Step 5: Calculate the pressure required to maintain the flow
- The pressure required to maintain the flow can be calculated using Bernoulli's equation: P + 1/2ρv^2 + ρgh = constant
- Since the tube is horizontal, the height difference (h) between the two ends is zero. Thus, the equation simplifies to: P + 1/2ρv^2 = constant
- Rearranging the equation, P = constant - 1/2ρv^2
- The density of water (ρ) is approximately 1000 kg/m^3
- Substituting the values, P = constant - 1/2 × 1000 kg/m^3 × (3.98 m/second)^2
Step 6: Convert pressure to the height of the mercury column
- The pressure required can be converted to the height of the mercury column using the equation: P = ρgh
- Rearranging the equation, h = P / (ρg)
- The density of mercury (ρ) is approximately 13,600 kg/m^3
- The acceleration due to gravity (g) is approximately 9.8 m/s^2
- Substituting the values, h = (P / (13,600 kg/m^3 × 9.8 m/s^2)) × (1 m / 100 cm)
Step 7: Calculate the final pressure in terms of the height of the mercury column
- Substitute the value of P from step 5 into the equation obtained in step 6 to calculate the final pressure in terms of the height of the mercury column.
Given:
- Length of the tube = 4 km = 4000 m
- Radius of the tube = 4 cm = 0.04 m
- Rate of water flow = 20 liters/second
Step 1: Convert the given measurements
- Convert the length of the tube from kilometers to meters: 4 km = 4000 m
- Convert the radius of the tube from centimeters to meters: 4 cm = 0.04 m
Step 2: Calculate the cross-sectional area of the tube
- The cross-sectional area (A) of a tube can be calculated using the formula: A = πr^2, where r is the radius of the tube.
- Substituting the given values, A = π(0.04)^2 = 0.0016π m^2
Step 3: Calculate the volume of water flowing per second
- The volume of water flowing per second can be calculated using the formula: Volume = flow rate × time
- Substituting the given values, Volume = 20 liters/second = 0.02 m^3/second
Step 4: Calculate the velocity of water flow
- The velocity (v) of water flow can be calculated using the formula: v = Volume / A
- Substituting the calculated values, v = (0.02 m^3/second) / (0.0016π m^2) ≈ 3.98 m/second
Step 5: Calculate the pressure required to maintain the flow
- The pressure required to maintain the flow can be calculated using Bernoulli's equation: P + 1/2ρv^2 + ρgh = constant
- Since the tube is horizontal, the height difference (h) between the two ends is zero. Thus, the equation simplifies to: P + 1/2ρv^2 = constant
- Rearranging the equation, P = constant - 1/2ρv^2
- The density of water (ρ) is approximately 1000 kg/m^3
- Substituting the values, P = constant - 1/2 × 1000 kg/m^3 × (3.98 m/second)^2
Step 6: Convert pressure to the height of the mercury column
- The pressure required can be converted to the height of the mercury column using the equation: P = ρgh
- Rearranging the equation, h = P / (ρg)
- The density of mercury (ρ) is approximately 13,600 kg/m^3
- The acceleration due to gravity (g) is approximately 9.8 m/s^2
- Substituting the values, h = (P / (13,600 kg/m^3 × 9.8 m/s^2)) × (1 m / 100 cm)
Step 7: Calculate the final pressure in terms of the height of the mercury column
- Substitute the value of P from step 5 into the equation obtained in step 6 to calculate the final pressure in terms of the height of the mercury column.
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Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column.
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Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column. for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column. covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column..
Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column. for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column. covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is flowing through a horizontal tube 4 km in length and 4 cm in radius at a rate of 20 litre per second. Calculate the pressure require to maintain the flow in terms of the height of mercury column..
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