Volume Flow Rate, Velocity, Factors

In summary, the question asks for the factor by which the flow rate decreases when a water pipe with a diameter of 20 cm and a flow rate of 10 cm/s splits into two smaller pipes with diameters of 11.54 cm and 16.33 cm. Using the equation Q=V*A, the flow rates for the smaller pipes are calculated to be 104.59 cm^3/s and 209.44 cm^3/s, respectively. To find the factor by which the flow rate decreases, it was necessary to use trial and error to determine which pair of factors matched the given flow rates.
  • #1
karmatic
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Homework Statement


By what factor does the flow rate decrease when a water pipe of diameter 20 cm with a 10 cms^-1 flow rate, splits into two smaller pipes of diameters 11.54 cm and 16.33 cm?


Homework Equations


Q(volume flow rate)=(average velocity)(cross sectional area of flow)


The Attempt at a Solution


Q=(10cm/s^-1)(1/4*3.14*(20cm)^2)
Q=314.16cm^3/s

Q=(10cm/s^-1)(1/4*3.14*(11.54cm)^2)
Q=104.59cm^3/s

Q=(10cm/s^-1)(1/4*3.14*(16.33cm)^2)
Q=209.44cm^3/s

Just in case anyone is wondering, the "flow rate" stated in the problem question is actually the velocity (I had to clarify that with my teacher). I think I have the flow rates calculated correctly, but I am unsure of how to go about working out what factor the flow rate is decreasing by for each of the smaller pipes. The answer is a multiple choice question so it was a simple process of trial and error to work out which pair of factors worked for the problem, but is there a way of showing how I would work that out without the multiple choice aspect? I want to be able to show as much working as possible! Thanks in advance :)
 
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  • #2
hey man I am actually doing teh same question how did u go about the guess and check to find out which one ?
 

What is volume flow rate and how is it measured?

Volume flow rate is the amount of fluid that passes through a given area per unit time. It is typically measured in cubic meters per second (m3/s) or liters per second (L/s). This can be measured using various instruments such as flow meters or by calculating the cross-sectional area of a pipe or channel and the velocity of the fluid.

What is velocity and how does it relate to volume flow rate?

Velocity is the rate of change of an object's position with respect to time. In fluid dynamics, it refers to the speed at which a fluid is moving. The volume flow rate is directly proportional to the velocity of the fluid, meaning that as the velocity increases, the volume flow rate also increases. This relationship is described by the equation Q = A x V, where Q is the volume flow rate, A is the cross-sectional area, and V is the velocity.

What are some factors that can affect volume flow rate?

Some factors that can affect volume flow rate include the viscosity of the fluid, the size and shape of the conduit through which the fluid is flowing, and the pressure difference between the two ends of the conduit. Other factors such as temperature, density, and turbulence can also have an impact on volume flow rate.

How is volume flow rate used in real-world applications?

Volume flow rate is an important concept in many industries, including water supply and treatment, oil and gas production, and manufacturing. It is used to monitor and control the flow of fluids through pipes and channels, ensuring that the correct amount of fluid is delivered to a specific location at a specific time. In medical settings, volume flow rate is also used to measure blood flow in arteries and veins.

How can volume flow rate be calculated in a system with changing velocities?

In a system with changing velocities, the volume flow rate can be calculated by dividing the total change in volume by the total change in time. This can be done by dividing the system into smaller sections and calculating the volume flow rate for each section, then adding them together to get the total volume flow rate for the entire system. Alternatively, the average velocity can be used in the equation Q = A x V, where A is the average cross-sectional area and V is the average velocity.

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