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The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)?
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The flow of blood in a large artery of an anesthetised dog is diverted...
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The flow of blood in a large artery of an anesthetised dog is diverted...
Flow of Blood in a Venturimeter:
To determine the speed of blood flow in an artery using a venturimeter, we need to apply the principles of fluid dynamics. A venturimeter is a device that measures fluid flow rate by utilizing the principle of conservation of mass.
Principle of Conservation of Mass:
According to the principle of conservation of mass, the mass of fluid entering a section of a pipe or tube must be equal to the mass of fluid leaving that section. This principle can be expressed mathematically as:
ρ₁A₁v₁ = ρ₂A₂v₂
Where:
- ρ₁ and ρ₂ are the densities of the fluid at two different sections of the venturimeter
- A₁ and A₂ are the cross-sectional areas of the wider and narrower parts of the meter, respectively
- v₁ and v₂ are the velocities of the fluid at the wider and narrower parts of the meter, respectively
Applying the Principle:
In this case, the wider part of the venturimeter has a cross-sectional area equal to that of the artery (A = 8 mm²), and the narrower part has an area (a = 4 mm²). The pressure drop in the artery is given as 24 Pa, and the density of blood is 1060 kg/m³.
We can assume that the density of blood remains constant throughout the venturimeter, and therefore, ρ₁ = ρ₂ = 1060 kg/m³.
Using the principle of conservation of mass, we can equate the mass flow rates at the wider and narrower sections of the venturimeter:
A₁v₁ = a*v₂
Calculating the Speed of Blood Flow:
To calculate the speed of blood flow in the artery, we need to rearrange the equation:
v₁ = (a/A₁)*v₂
Substituting the given values:
v₁ = (4 mm² / 8 mm²)*v₂
v₁ = 0.5*v₂
Now, we can calculate the speed of blood flow at the narrower section of the venturimeter using the pressure drop:
ΔP = 0.5*ρ₂*v₂² - 0.5*ρ₁*v₁²
Since ρ₁ = ρ₂ = 1060 kg/m³, the equation simplifies to:
ΔP = 0.5*ρ*v₂² - 0.5*ρ*(0.5*v₂)²
ΔP = 0.5*ρ*v₂² - 0.25*ρ*v₂²
ΔP = 0.25*ρ*v₂²
Substituting the given pressure drop ΔP = 24 Pa and ρ = 1060 kg/m³:
24 = 0.25*1060*v₂²
Simplifying the equation:
v₂² = 24 / (0.25*1060)
v₂² = 0.0226415
v₂ ≈ √0.0226415
v₂ ≈ 0.1503 m/s
Finally, we can calculate the speed of blood flow in the artery:
v₁ = 0.5*v₂
v₁ = 0.5*0.1503
v₁
To determine the speed of blood flow in an artery using a venturimeter, we need to apply the principles of fluid dynamics. A venturimeter is a device that measures fluid flow rate by utilizing the principle of conservation of mass.
Principle of Conservation of Mass:
According to the principle of conservation of mass, the mass of fluid entering a section of a pipe or tube must be equal to the mass of fluid leaving that section. This principle can be expressed mathematically as:
ρ₁A₁v₁ = ρ₂A₂v₂
Where:
- ρ₁ and ρ₂ are the densities of the fluid at two different sections of the venturimeter
- A₁ and A₂ are the cross-sectional areas of the wider and narrower parts of the meter, respectively
- v₁ and v₂ are the velocities of the fluid at the wider and narrower parts of the meter, respectively
Applying the Principle:
In this case, the wider part of the venturimeter has a cross-sectional area equal to that of the artery (A = 8 mm²), and the narrower part has an area (a = 4 mm²). The pressure drop in the artery is given as 24 Pa, and the density of blood is 1060 kg/m³.
We can assume that the density of blood remains constant throughout the venturimeter, and therefore, ρ₁ = ρ₂ = 1060 kg/m³.
Using the principle of conservation of mass, we can equate the mass flow rates at the wider and narrower sections of the venturimeter:
A₁v₁ = a*v₂
Calculating the Speed of Blood Flow:
To calculate the speed of blood flow in the artery, we need to rearrange the equation:
v₁ = (a/A₁)*v₂
Substituting the given values:
v₁ = (4 mm² / 8 mm²)*v₂
v₁ = 0.5*v₂
Now, we can calculate the speed of blood flow at the narrower section of the venturimeter using the pressure drop:
ΔP = 0.5*ρ₂*v₂² - 0.5*ρ₁*v₁²
Since ρ₁ = ρ₂ = 1060 kg/m³, the equation simplifies to:
ΔP = 0.5*ρ*v₂² - 0.5*ρ*(0.5*v₂)²
ΔP = 0.5*ρ*v₂² - 0.25*ρ*v₂²
ΔP = 0.25*ρ*v₂²
Substituting the given pressure drop ΔP = 24 Pa and ρ = 1060 kg/m³:
24 = 0.25*1060*v₂²
Simplifying the equation:
v₂² = 24 / (0.25*1060)
v₂² = 0.0226415
v₂ ≈ √0.0226415
v₂ ≈ 0.1503 m/s
Finally, we can calculate the speed of blood flow in the artery:
v₁ = 0.5*v₂
v₁ = 0.5*0.1503
v₁
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The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)?
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The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)?.
The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter.The wider part of the meter has a cross sectional area equal to that of artery , A=8mm² narrower part has an area a=4mm².The pressure drop in the artery is 24 Pa. What is the speed of blood flow in artert? (density of blood is 1060 kgm-³)?.
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