Water Pressure Velocity Acceleration (dv/dt)

In summary, water pressure velocity acceleration (dv/dt) is a measure of the change in velocity of water over time and is an important concept in fluid dynamics. It is calculated by taking the derivative of the velocity function with respect to time and can be affected by factors such as container shape and size, water viscosity, and external forces. This concept is important in science because it helps us understand the behavior of fluids, and it has various real-life applications in fields such as engineering, meteorology, and industrial processes.
  • #1
Steve Page
2
0
I am having trouble solving this problem. Any assistance is greatly appreciated.

Water is discharged from a pipeline at a velocity of v given by v=1192p^(1/2), where p is the pressure (in psi). If the water pressure is changing at a rate of 404 psi/second, find the acceleration (dv/dt) of the water when p = 34 psi.

I have soved the v' to equal: 596p^(-.5).
Does dv/dt = 596^(-.5)/t for (dv/dt)?
What's the next step?
 
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  • #2
Welcome to PF!

Hi! Steve Welcome to PF! :smile:

Use the chain rule :wink:
 
  • #3
Thanks Tniy-Tim!
 

What is water pressure velocity acceleration (dv/dt)?

Water pressure velocity acceleration (dv/dt) is a measure of the change in velocity of water over time. It is used to describe the rate at which the speed of water is changing, and is an important concept in fluid dynamics.

How is water pressure velocity acceleration (dv/dt) calculated?

Water pressure velocity acceleration (dv/dt) is calculated by taking the derivative of the velocity function with respect to time. This can be done using calculus, and the resulting value is expressed in units of meters per second squared (m/s²).

What factors affect water pressure velocity acceleration (dv/dt)?

There are several factors that can affect water pressure velocity acceleration (dv/dt), including the shape and size of the container, the viscosity of the water, and the force acting on the water. Additionally, changes in temperature and the presence of other substances in the water can also impact the velocity and acceleration.

Why is water pressure velocity acceleration (dv/dt) important in science?

Water pressure velocity acceleration (dv/dt) is important in science because it helps us understand the behavior of fluids, including water. By studying how the velocity and acceleration of water change over time, we can better understand the physical properties of water and how it interacts with other substances.

How is water pressure velocity acceleration (dv/dt) used in real life?

Water pressure velocity acceleration (dv/dt) has many practical applications in real life. For example, it is used in designing water systems and plumbing, understanding the movement of water in rivers and oceans, and predicting the behavior of fluids in industrial processes. It is also important in fields such as meteorology, where it helps us understand weather patterns and the movement of water in the atmosphere.

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