How Does Water Flow Rate Change Over Time in a Draining Cylinder?

In summary, the height of the cylinder is 5.5 meters with a radius of 1 meter. There is a hole with a radius of .02 meters located .5 meters from the bottom (5 meters from the top). The question asks for the rate of change of the flowrate (dflowrate/dt) and the height (dh/dt). The equation for the volume of fluid in the cylinder is V(t) = h(t)πR^2.
  • #1
unsung-hero
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Homework Statement


Ok, so the height of the cylinder is 5.5 meters. The radius is 1 meters.
There is a hole, .5 meters from the bottom(5 meters from the top), its radius is .02 meters.

The question is how fast does water flow out, relative to time(this because the height of the water keeps dropping, so the flow rate decreases). [/B]

Thank You :)

Homework Equations


Am i doing it right?
If i am, can you please solve it(i can't quiet figure it out)?
Please give the rate of change of the flowrate(dflowrate/dt).
Also, rate of change of height(dh/dt).
[/B]

The Attempt at a Solution


Height = total volume - (integral sign) flowrate dt
flowrate = (cross sectional area * Velocity(
18632c090016d6d87c3f7653a95cf02a.png
) * density

dflowrate/dt = (deritive of the expression above)[/B]
 
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  • #2
Suppose that h(t) is the height of the fluid level in the cylinder at time t, and R is the radius of the cylinder. What is the volume of fluid in the cylinder V(t) at time t?

Chet
 

FAQ: How Does Water Flow Rate Change Over Time in a Draining Cylinder?

1. What factors affect the rate of water flow out of a cylinder?

The rate of water flow out of a cylinder can be affected by several factors, including the diameter of the cylinder, the height of the water level in the cylinder, the pressure of the water, and the viscosity of the water.

2. How can I calculate the flow rate of water out of a cylinder?

The flow rate of water out of a cylinder can be calculated using the equation Q = A x V, where Q is the flow rate, A is the cross-sectional area of the cylinder, and V is the velocity of the water. The velocity can be calculated using Bernoulli's equation, which takes into account the pressure and height of the water in the cylinder.

3. How does the shape of the cylinder affect the flow of water?

The shape of the cylinder can affect the flow of water in terms of resistance and turbulence. A cylinder with a smoother surface will experience less resistance and therefore have a higher flow rate. A cylinder with a more streamlined shape will also have less turbulence and a more consistent flow rate.

4. Does the temperature of the water affect the flow rate out of a cylinder?

Yes, the temperature of the water can affect the flow rate out of a cylinder. This is because as temperature increases, the viscosity of water decreases, allowing it to flow more easily. Therefore, warmer water will have a higher flow rate compared to colder water.

5. How does gravity impact the flow of water out of a cylinder?

Gravity plays a significant role in the flow of water out of a cylinder. The force of gravity pulls the water down, creating pressure at the bottom of the cylinder. This pressure, along with the height of the water, determines the velocity of the water as it flows out of the cylinder.

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