Name: spray tank pipe flow rate calculation
Uploaded: 2025-02-13T15:43:36.000Z
Duration: 1 min 28 s
Channel: JoVE

Consider a spray tank system designed to evenly apply pest-control liquid to plants.
The system includes a pressurized tank at 150 kPa filled with pesticide to a height of 0.80 m.
A 1.9 m long pipe with a 0.015 m diameter, inclined at 0.698 radians, connects the tank to a 0.0075 m nozzle.
The objective is to calculate the flow rate; to achieve this, the flow velocity in the pipe is first determined and then used to find the flow rate.
The initial flow velocity in the pipe at Point 1 is zero, and the pressure at Point 2, located at the nozzle, is zero.
The nozzle height above the bottom of the tank is calculated based on the pipe&#39;s inclination.
The flow rate equation establishes a relationship between the flow velocity in the pipe and at the nozzle.
The modified Bernoulli equation incorporates friction and a loss coefficient to link parameters at Points 1 and 2.
After substituting values for the known parameters, the flow velocity in the pipe is determined.
This velocity, multiplied by the cross-sectional area, is then used to calculate the flow rate, ensuring precise application.

pipe flowrate measurement: problem solving

Pipe Flowrate Measurement: Problem Solving

A spray tank system is engineered to uniformly distribute a pest-control liquid across plants by using a pressurized mechanism. The tank, pressurized to 150 kPa, holds the pesticide at a height of 0.80 meters. Liquid flows from the tank through a 1.9 meter pipe with a diameter of 0.015 meters, angled at 0.698 radians, ultimately reaching a 0.007 meter nozzle that sprays the pesticide. Accurate calculation of the system's flow rate is crucial to ensure uniform application, and this is achieved by first determining the flow velocity within the connecting pipe.
The design requires an understanding of fluid mechanics principles. At the outset, the velocity of the fluid in the tank at Point 1 is zero, with the pressure set to 150 kPa. Point 2, located at the nozzle, is assumed to be open to the atmosphere, with a pressure of zero. The height difference between Points 1 and 2, calculated using the 0.698-radian pipe angle and pipe length, determines the elevation change component in the Bernoulli equation. This height difference is found by multiplying the pipe length by the sine of the inclination angle.
To connect the parameters at Points 1 and 2, a modified Bernoulli equation is used, accounting for energy losses due to friction and the nozzle's loss coefficient. The equation expresses the pressure, velocity, and elevation terms for both points as follows:
<img alt="Bernoulli's equation; fluid dynamics formula; pressure, velocity, height; energy conservation." src="/files/ftp_upload/18085/18085_PT_equation_1.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Here, p represents pressure, &#961; the fluid density, V the velocity, g the gravitational acceleration, z1 the height of the pesticide inside the tank, and z2 the nozzle height above the bottom of the tank. With values substituted for these terms, the flow velocity in the pipe at Point 1 is solved.
After calculating the pipe's flow velocity, the flow rate, Q, is determined by multiplying this velocity by the cross-sectional area A of the pipe:
<img alt="Fluid flow equation Q=AV; formula for flow rate calculation; mathematical concept." src="/files/ftp_upload/18085/18085_PT_equation_2.svg" style="text-align: center; height: 11px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
Where A is:
<img alt="Area formula, A=&#960;D&#178;/4, mathematical equation, circle area calculation." src="/files/ftp_upload/18085/18085_PT_equation_3.svg" style="text-align: center; height: 25px;" data-altupdatedat="1762173717000" data-alt="Equation 3" />
This flow rate calculation ensures that the pesticide is delivered at a consistent and effective rate, optimizing pest control application.

Consider a spray tank system designed to evenly apply pest-control liquid to plants.
The system includes a pressurized tank at 150 kPa filled with ...

pipe-flowrate-measurement-problem-solving

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JoVE Core

Civil Engineering

Unit 1

Flow in Pipes

KEY TERMS AND CONCEPTS

spray tank pipe flow rate calculation

Spray tank pipe flow rate calculation uses fluid mechanics to find how fast pesticide moves through a pressurized system. The tank is pressurized to 150 kPa and holds the liquid at a height of 0.80 meters. The liquid then travels through a 1.9 meter pipe with a diameter of 0.015 meters and an angle of 0.698 radians before reaching a 0.007 meter nozzle that sprays the pesticide.

Accurate flow rate matters because the pesticide must be applied evenly across the plants. The first step is to find the flow velocity in the pipe. At Point 1, the fluid in the tank starts with zero velocity and a pressure of 150 kPa. At Point 2, the nozzle is open to the atmosphere, so the pressure there is taken as zero.

The height change between Points 1 and 2 also affects the calculation. That change comes from the pipe length and angle, and it is found by multiplying the 1.9 meter pipe length by the sine of 0.698 radians. A modified Bernoulli equation is then used to connect pressure, velocity, and elevation at both points. This form also includes energy losses from friction and the nozzle loss coefficient.

In the equation, p stands for pressure, ρ is fluid density, V is velocity, g is gravitational acceleration, z1 is the pesticide height inside the tank, and z2 is the nozzle height above the bottom of the tank. After substituting the given values, the pipe flow velocity at Point 1 can be solved. The flow rate, Q, is then found by multiplying that velocity by the pipe cross-sectional area A. This calculation helps the spray system deliver pesticide at a steady and effective rate.

Spray Tank Pipe Flow Rate Calculation

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Spray tank pipe flow rate calculation uses fluid mechanics to find how fast pesticide moves through a pressurized system. The tank is pressurized to 150 kPa and holds the liquid at a height of 0.80 meters. The liquid then travels through a 1.9 meter pipe with a diameter of 0.015 meters and an angle of 0.698 radians before reaching a 0.007 meter nozzle that sprays the pesticide. Accurate flow rate matters because the pesticide must be applied evenly across the plants. The first step is to find...

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key terms and concepts

Solve a spray tank flow rate problem using Bernoulli’s equation, pipe angle, nozzle losses, and pipe area to find pesticide flow in a pressurized system.

Spray Tank Pipe Flow Rate Calculation | JoVE K12

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civil engineering

Spray Tank Pipe Flow Rate Calculation

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