Decay constant for water flow

In summary: No. I'm just wondering if hydro static pressure has an effect on the rate of flow of water. I'd assume that at peak volume, the hydro static pressure is higher and so the rate is fast and as the volume decreases, the pressure does so as well and so the rate decreases. Is this right?Yes, that is correct.
  • #1
Saado
44
0
When modelling exponential decay in class we did a water flow through a burette experiment. We were given the equation V(t)= V0 e^-λt and ln(V0/V)=λt Where lambda is the decay constant, V0 is the initial volume and V is the volume at any time t. What does the decay constant actually tell you in this situation? I know it's measured in 1/seconds but what does it show you?
 
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  • #2
The inverse of the decay constant is proportional to the half life (The time to lose half of the volume in the experiment)
 
  • #3
Thank you. A follow up question. As the volume decreases as the water flows out, the rate at which the water flows out also decreases. Is this because there is less hydro-static pressure on the water?
 
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  • #4
dauto said:
The inverse of the decay constant is proportional to the half life (The time to lose half of the volume in the experiment)

Not quite the formal definition of the decay constant, but of the half life time constant, which uses the exponential of 2, and not e.

From the equation V(t)= Vo e^-λt , or V(t)/Vo = e^-λt,
one can see that if the exponent λt = 1,
then,
V(t)/Vo = 1/e = 0.3678 ..

In other words the initial value Vo has decayed to 1/e of its value after one decay constant.
 
  • #5
256bits said:
Not quite the formal definition of the decay constant, but of the half life time constant, which uses the exponential of 2, and not e.

From the equation V(t)= Vo e^-λt , or V(t)/Vo = e^-λt,
one can see that if the exponent λt = 1,
then,
V(t)/Vo = 1/e = 0.3678 ..

In other words the initial value Vo has decayed to 1/e of its value after one decay constant.

That's why I didn't say they are equal. I said they are proportional.
 
  • #6
Anything on the hydro static pressure? :P
 
  • #7
Saado said:
Anything on the hydro static pressure? :P
Are you asking for a derivation of that equation, with λ related to actual physical parameters?

Chet
 
  • #8
No. I'm just wondering if hydro static pressure has an effect on the rate of flow of water. I'd assume that at peak volume, the hydro static pressure is higher and so the rate is fast and as the volume decreases, the pressure does so as well and so the rate decreases. Is this right?
 
  • #9
Saado said:
No. I'm just wondering if hydro static pressure has an effect on the rate of flow of water. I'd assume that at peak volume, the hydro static pressure is higher and so the rate is fast and as the volume decreases, the pressure does so as well and so the rate decreases. Is this right?
Suppose you have a valve at the bottom of the column, and the characteristic of this valve is that Q = k(P-P0), where Q is the volume rate of flow out the valve, and P-P0 is the pressure drop across the valve. Assume that this is the dominant flow resistance in the system. Also, the pressure at the bottom of the column is P0+ρgz. Then a mass balance on the column gives:

[tex]\frac{dV}{dt}=-kρgz=-\frac{kρg}{A}V[/tex]

where A is the cross sectional area of the column.

Chet
 

What is the decay constant for water flow?

The decay constant for water flow is a measure of how quickly water will decrease in volume or flow rate over time. It is often used to describe the rate of decay in water supply systems.

How is the decay constant for water flow calculated?

The decay constant for water flow is calculated by dividing the natural logarithm of the initial flow rate by the natural logarithm of the final flow rate. This is often expressed as a negative value, indicating the decrease in water flow over time.

What factors can affect the decay constant for water flow?

The decay constant for water flow can be affected by a variety of factors, including temperature, pressure, and the presence of impurities or contaminants in the water. These can all impact the rate at which the water decreases in flow over time.

Why is the decay constant for water flow important in water supply systems?

The decay constant for water flow is important in water supply systems because it helps ensure the proper functioning and efficiency of the system. By understanding the rate at which water will decrease in flow, engineers and scientists can design and maintain systems that meet the needs of consumers without wasting resources.

Can the decay constant for water flow be changed?

The decay constant for water flow is generally considered to be a fixed value for a given system. However, certain factors such as changes in temperature or pressure can affect the decay rate and may require adjustments to the system to maintain optimal flow rates. Additionally, regular maintenance and cleaning can help prevent buildup and prolong the life of a water supply system, potentially impacting the decay constant over time.

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