Calculating Air Pressure, Velocity at Venturi Tube Inlet/Throat/Outlet

In summary: V3)^2At the outlet (point 3):P3 = P4 + (1/2)(1.225)(V4)^2 = P4 + 0. Therefore, P3 = P4.Next, we can use the continuity equation, which states that the mass flow rate is constant throughout the flow, to find the local velocity at each point:ρ1V1A1 = ρ2V2A2 = ρ3V3A3Since the air density is constant, we can cancel it out:V1A1 = V2A2 = V3A3At the inlet (point 1):V1 = V2 =
  • #1
PilotKen
1
0
Im a new to this site because my have a question that i don't know how to answer and it really confusing me. If it possible, can you guys show me step by step on how to solve it.

A venturi tube has an inlet diameter of 3.0 inches, a throat diameter of 1.5 inches and an outlet diameter of 3.5 inches. (at standard day conditions and sea level).
What is the local air pressure, dynamic pressure, total pressure and local velocity at the inlet, throat and outlet point.
 
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  • #2
please cosult this book for ur numerical" fluid mechanics" by RK rajput
 
  • #3


Hi there! Welcome to the forum. I'd be happy to help you with your question.

To solve this problem, we will use the Bernoulli's equation, which states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid is constant throughout the flow.

First, let's define some variables:
- P: local air pressure (in Pa)
- ρ: air density (in kg/m^3)
- V: local velocity (in m/s)
- A: cross-sectional area (in m^2)

To find the local air pressure at each point, we can use the equation:
P + (1/2)ρV^2 = constant
Since we are dealing with standard day conditions and sea level, we can assume that the air density is constant at 1.225 kg/m^3.

At the inlet (point 1):
P1 + (1/2)(1.225)(V1)^2 = P2 + (1/2)(1.225)(V2)^2
Since the inlet diameter is 3.0 inches, the cross-sectional area is A1 = π(3/2)^2 = 7.065 m^2.
Since the air is at rest at the inlet, V1 = 0.
At the throat (point 2):
P2 + (1/2)(1.225)(V2)^2 = P3 + (1/2)(1.225)(V3)^2
Since the throat diameter is 1.5 inches, the cross-sectional area is A2 = π(1.5/2)^2 = 1.7675 m^2.
At the outlet (point 3):
P3 + (1/2)(1.225)(V3)^2 = P4 + (1/2)(1.225)(V4)^2
Since the outlet diameter is 3.5 inches, the cross-sectional area is A3 = π(3.5/2)^2 = 9.621 m^2.

Now, we can solve for the local air pressure at each point:
At the inlet (point 1):
P1 = P2 + (1/2)(1.225)(V2)^2 = P2 + 0. Therefore, P1 = P2.
At the throat (point 2):
P2 = P3 + (1
 

What is the Venturi effect and how does it relate to air pressure and velocity?

The Venturi effect is the phenomenon where the velocity of a fluid increases as it passes through a constricted section of a pipe, while the pressure decreases. This is due to the conservation of energy principle, where the total energy of the fluid remains constant, but the velocity increases as the cross-sectional area decreases.

How do you calculate air pressure at the inlet, throat, and outlet of a Venturi tube?

The air pressure at the inlet, throat, and outlet of a Venturi tube can be calculated using the Bernoulli's equation, which states that the total energy of a fluid remains constant. This equation takes into account the density, velocity, and height of the fluid at each point in the tube. By solving for the pressure at each point, the air pressure can be determined.

What factors affect the velocity of air at the inlet, throat, and outlet of a Venturi tube?

The velocity of air at the inlet, throat, and outlet of a Venturi tube is affected by several factors. These include the cross-sectional area of the tube, the fluid density, and the pressure difference between the inlet and outlet. Additionally, the shape and smoothness of the tube can also play a role in determining the velocity of air.

How can the velocity of air at the inlet, throat, and outlet of a Venturi tube be measured?

The velocity of air at the inlet, throat, and outlet of a Venturi tube can be measured using a variety of methods, such as using a pitot tube or a hot-wire anemometer. These instruments measure the pressure and velocity at different points in the tube and can be used to calculate the velocity of air at each point.

What are some practical applications of using a Venturi tube to measure air pressure and velocity?

Venturi tubes are commonly used in various industries, such as in HVAC systems, to measure and control air flow. They are also used in aircrafts and automobiles to measure air speed. Additionally, Venturi tubes are used in water treatment plants to measure and regulate the flow of water. They are also used in medical devices, such as nebulizers, to accurately measure and control the flow of medication.

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