Speed of water and height involving fluid mechanics

In summary, a problem involving a large closed tank with a water nozzle is discussed. The absolute pressure of the air above the water is given and the goal is to find the speed at which the water leaves the nozzle and the height to which the water rises. The solution involves using energy conservation and kinematic equations, assuming the nozzle is very small. If the nozzle has a finite size, Bernoulli's equation and the equation of continuity must also be applied.
  • #1
physicsdreams
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Homework Statement



In a very large closed tank, the absolute pressure of the air above the water is 6.01x10^5 Pa. The water leaves the bottom of the tank through a nozzle that is directed straight upward. The opening of the nozzle is 4.00m below the surface of the water. a) Find the speed at which the water leaves the nozzle. b) Ignoring air resistance and viscous effects, determine the height to which the water rises.

Thanks!

Homework Equations



P+rhov^2/2+rhogh= constant

P2=P1+rhogh

kinematics?


The Attempt at a Solution



I know that I can set the initial height to zero, but that's about it. I really don't know how to treat this problem.
 
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  • #2
Use energy conservation to get velocity(u) of water just outside nozzle.You will get u=sqrt(2gs). Assuming nozzle is very small.Here s is distance of nozzle from topmost layer of water(4.00m). After getting velocity use kinematic equation (v^2)=(u^2)-2gh.
For highest point v=0.Thus getting h=u^2/2g.
Which is same as s(4.00m) as it should be from energy conservation(similar to ball thrown in air and returning back to Earth and again reaching same height h after colliding from ground(assuming it to be elastic collision).
 
  • #3
1994Bhaskar said:
Use energy conservation to get velocity(u) of water just outside nozzle.You will get u=sqrt(2gs).

Can you show me what the entire (energy conservation) equation is before you simplified it?
Is it Bernoulli's equation?

thanks
 
  • #4
Just take a small element of water of mass dm at a height s above the nozzle.
Initial energy=Potential Energy=dm*g*h
Final energy after just coming out from nozzle(assuming it to be at height 0)=0.5*dm*u^2
Equating final and initial energy you can get u=sqrt(2gs).
Here however we assume that nozzle is very small and let's only point particles out.Only then we can do mechanical energy conservation.
 
  • #5
Can you tell me that what would you do if nozzle is not very small, i.e. it has a small area 'a' and let's finite amount of water out(not point sized particles)??You also know area of topmost layer of water as 'A'.
Think it yourself.The answer becomes more interesting.
Hint:In that case don't apply energy conservation.You will apply only equations of fluids-->
Bernoulli and Equation of continuity.
 

What is the relationship between the speed of water and its height in fluid mechanics?

The speed of water and its height are inversely proportional in fluid mechanics. This means that as the height of the water decreases, the speed of the water increases, and vice versa. This relationship is known as the continuity equation.

How does the speed of water affect the pressure in fluid mechanics?

In fluid mechanics, the speed of water is directly proportional to the pressure. This means that as the speed of water increases, the pressure also increases. This relationship is known as Bernoulli's principle.

What factors can affect the speed of water in fluid mechanics?

The speed of water in fluid mechanics can be affected by various factors such as the viscosity of the fluid, the surface tension, and the flow rate. Other factors like the shape and size of the container can also impact the speed of water.

How can the speed of water be measured in fluid mechanics?

The speed of water in fluid mechanics can be measured using various instruments such as a pitot tube, a flow meter, or by using the continuity equation. These methods can provide accurate measurements of the speed of water in a given system.

What are some real-life applications of understanding the speed of water in fluid mechanics?

Understanding the speed of water in fluid mechanics is crucial in various industries such as hydraulics, plumbing, and irrigation. It is also essential in designing efficient water transportation systems, dams, and water turbines. Additionally, it is used in weather forecasting and oceanography to study the movement of water in the atmosphere and oceans.

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