Past paper question about rates

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In summary, the conversation discusses the problem of determining the water velocity and tank fill level in a system where water is entering a large tank at a rate of 0.2m^3s^-1 and leaving through a small hole with an area of 0.05m^2. The equation v*Area = v*0.05 is used to find the rate of water leaving the tank, but it is noted that the two rates may not be the same except in the steady state. The conversation ends with a question about the units and how to change the equation for velocity*area.
  • #1
captainjack2000
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Homework Statement


Water is falling gently into a large tank at 0.2m^3s^-1 and leaves through a small hole in the bottom of the tank of area 0.05m^2. What is the water velocity as it leaves? How full is the tank in the steady state?




Homework Equations


Well if the rate of water entering is 0.2m^3s^-1 by dimensional analysis rate=velocity*area
So the rate of water leaving the tank will be v*Area = v*0.05

I'm not sure how to find the velocity of the water as it leaves the tank because surely these two rates will not be the same (except in the steady state??)
 
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  • #2
captainjack2000 said:

Homework Statement


Water is falling gently into a large tank at 0.2m^3s^-1 and leaves through a small hole in the bottom of the tank of area 0.05m^2. What is the water velocity as it leaves? How full is the tank in the steady state?


Homework Equations


Well if the rate of water entering is 0.2m^3s^-1 by dimensional analysis rate=velocity*area
So the rate of water leaving the tank will be v*Area = v*0.05

I'm not sure how to find the velocity of the water as it leaves the tank because surely these two rates will not be the same (except in the steady state??)
You've almost got it.

What is v * Area? or rather what are the units of v * A?
 
Last edited:
  • #3
sorry what do you mean
how to do change velocity*area?
 

Related to Past paper question about rates

What is the definition of rate?

A rate refers to the change in one quantity in relation to another quantity. It is typically expressed in units of time, such as miles per hour or liters per minute.

What are the different types of rates?

There are two main types of rates: average rate and instantaneous rate. Average rate refers to the change in a quantity over a period of time, while instantaneous rate refers to the rate at a specific point in time.

How do you calculate a rate?

To calculate a rate, you need to determine the change in the quantity of interest and the corresponding change in time. The rate is then expressed as the change in quantity over the change in time.

What factors can affect the rate of a process?

The rate of a process can be affected by various factors, such as temperature, concentration, pressure, and the presence of catalysts. These factors can either increase or decrease the rate of a process.

Why is it important to understand rates in science?

Understanding rates is crucial in science as it allows us to analyze and predict the behavior of systems and processes. It also helps us to optimize processes and develop new technologies that can improve efficiency and productivity.

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