Average speed of the gasoline as it leaves the nozzle?

In summary: I am here to help.In summary, the problem involves filling a gas tank with a volume of 40 liters in 2 minutes. The nozzle has a radius of 1cm and the goal is to find the average speed of the gasoline as it leaves the nozzle. Using the equation Q=v*A, where Q is the flow rate in cm^3/s and A is the cross-sectional area, we can find the velocity of the liquid flow through the nozzle. The flow rate is found by taking the volume over time, and the velocity is found by dividing the flow rate by the cross-sectional area. The final answer is 1.1 meters per second.
  • #1
Punkyc7
420
0

Homework Statement


It takes 2 minutes to fill a gas tank with 40 liters of gasoline. If the nozzle is 1cm in radius, what is the average speed of the gasoline as it leaves the nozzle?


Homework Equations


A1V1=A2v2 or 1/2pv^2 + pgh+p=constant


The Attempt at a Solution


I don't really know were to start I have the volume of the tank as being .04m^3 I am not sure what to do next.
 
Last edited:
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  • #2


You want the flow rate equation.

Q=v*A

Where Q = flowrate in cm^3/s and A is the cross-sectional area.
 
  • #3


Why is the flow rate in cm^3/s wouldn't it be squared because of area.
A would be = to 3.14159265*10^-4
 
  • #4


Also the books says the anwser is 1.1 meters a second i just don't know how it got to that
 
  • #5


Volume V = X *A
V/t = X/t*A = v*A, where v is the velocity of the liquid flow through the nozzle.
 
  • #6


is that calculus because I haven't been taught how to use or apply it to these types of problems.
 
  • #7


NO. Not at all.
In the problem what is flow rate V/t?
If you freeze the outflow of one second, whose length is L and area of cross section is A, what is the volume of the liquid?
(L/one second) is the average velocity of out flow.
 
  • #8


the volume is .04m^3, cross sectional area is .01^2*pi
 
  • #9


dQ/dt = Volume/time. What is the time taken to fill the tank?
Velocity = (dQ/dt)/Area.
 
  • #10


Thanks i got it for some reason i couldn't get to that equation before but now i get it sorry for taking up your time.
 
  • #11


It is OK.
 

Related to Average speed of the gasoline as it leaves the nozzle?

1. What is the average speed of gasoline as it leaves the nozzle?

The average speed of gasoline as it leaves the nozzle can vary depending on several factors such as the type of gasoline, the nozzle design, and the pressure at which it is being pumped. However, on average, the speed can range from 10-15 meters per second.

2. How is the average speed of gasoline calculated?

The average speed of gasoline is calculated by dividing the volume of gasoline leaving the nozzle by the time it takes to leave. This calculation can be affected by the size of the nozzle opening, the pressure of the pump, and the viscosity of the gasoline.

3. Why is the average speed of gasoline important?

The average speed of gasoline is important because it can affect the efficiency of fueling and also impact the performance of the vehicle. A higher average speed can result in a faster fueling process and potentially improve the overall fuel economy of the vehicle.

4. How does the average speed of gasoline leaving the nozzle impact the environment?

The average speed of gasoline leaving the nozzle can impact the environment in several ways. A higher speed can create more air pollution as it can lead to more vapors being released. Additionally, if the speed is too high, it can pose a safety hazard and increase the risk of spills and leaks.

5. Can the average speed of gasoline leaving the nozzle be controlled?

Yes, the average speed of gasoline leaving the nozzle can be controlled by adjusting the pressure of the pump or using different nozzle designs. Some fuel stations also have regulations in place to limit the speed of gasoline leaving the nozzle for safety and environmental reasons.

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