How to Calculate Flow Rate in a Tapered Pipe with Pressure Difference?

In summary, the problem involves finding the volume flow rate of an alcohol through a tapered pipe with a pressure difference of 8.8 kPa. The relevant equations are used to derive the velocity of the alcohol and then solve for the volume flow rate.
  • #1
12342
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Homework Statement


An alcohol flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 = 43.7 cm2 to A2= A1/4. The pressure difference Δp between the wide and the narrow sections of the pipe is 8.8 kPa. What is the volume flow rate ΔV/Δt of the alcohol? The density of the alcohol is ρ = 796 kg/m3.


Homework Equations


I figured I would have to use:

v1 = sqrt( 2*deltap / 15(rho) )


The Attempt at a Solution



I'm not entirely sure how to start this. I'm very cinfused.

v^2
 
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  • #2
Hi 12342, welcome to PF.
The relevant equations are
P1 +1/2*ρ*v1^2 = P1 + 1/2*ρ*v2^2 ...(1)
And rat of flow
Q = A1*v1 = A2*v2...(2)
From the second equation find v2 in terms of v1 and put it in eq. 1. Then solve for v1and then Q.
 

1. What is flow rate and how is it measured?

Flow rate is the amount of fluid that passes through a given point in a specified amount of time. It is typically measured in units of volume per time, such as liters per second or gallons per minute. Flow rate can be measured using various instruments such as flow meters or by calculating it based on the velocity and cross-sectional area of the fluid.

2. What factors affect the flow rate of a fluid?

The flow rate of a fluid can be affected by various factors such as the viscosity of the fluid, the size and shape of the conduit or pipe through which it is flowing, the pressure difference between the two ends, and the temperature of the fluid. Other factors such as turbulence, density, and surface roughness can also have an impact on the flow rate.

3. How does flow rate impact the performance of a system?

The flow rate of a fluid is a crucial factor in determining the performance of a system. For example, in a hydraulic system, a higher flow rate can increase the power and speed of the system. In a chemical processing plant, the flow rate can affect the efficiency and productivity of the plant. A lower flow rate can also lead to problems such as clogging or inadequate cooling, while a higher flow rate can cause erosion or excessive energy consumption.

4. What are some common methods for controlling flow rate?

There are several methods for controlling flow rate, depending on the specific application. Some common methods include using valves or pumps to adjust the pressure and flow rate, using flow meters to monitor and regulate the flow, and using flow restrictors or orifices to limit the flow. Other methods such as changing the size or shape of the conduit, altering the temperature or viscosity of the fluid, or adjusting the speed of the fluid can also be used to control the flow rate.

5. How is flow rate related to other properties of a fluid?

Flow rate is closely related to other properties of a fluid such as viscosity, density, and velocity. For example, a fluid with a higher viscosity will typically have a lower flow rate, while a fluid with a lower density will have a higher flow rate. Additionally, an increase in velocity can lead to an increase in flow rate, while a decrease in velocity can decrease the flow rate. These relationships are important to consider when analyzing and controlling flow rate in various systems.

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