A Problem of my Own Device:

[vivekrai]

A cylindrical tank of radius " r " contains water upto height " H " . There is a hose at height " h " from the bottom. At what angle should the tank be inclined (Of course in the direction of the hose) so as to double the water output from the hose?

N.B. Assume necessary simplifications

 

[JaredJames]

What are your thoughts on this? We'll need your own input for homework style questions.

 

[vivekrai]

Homework type question? I don't think so. This idea came to while doing a work and don't why I'm compelled that it's solvable (and of course it is).

So I posted it here to fetch some idea on what concepts can be used and how so that I can sum up the complete process.

Please Reply If you have any helping ideas.

 

[JaredJames]

This is a textbook style question. Therefore it demands your attempt first.

There is no answer regarding 'tilting the tank'. This will have minimal effect on increase flow rate.

 

[vivekrai]

I haven't seen such question anywhere in any textbook. Any by the way, I know equations related to Fluid mechanics but I'm hopeless here on how to proceed or use the equation.

Cause In most cases, when I'm able to start I finish it well myself.

A bit edited question then :

A cylindrical tank of radius " r " contains water upto height " H " . There is a hose at height " h " from the bottom. At what angle should the tank be inclined (Of course in the direction of the hose) so as to increase the water output " m " times from the hose?

N.B. Assume necessary simplifications

 

[JaredJames]

I haven't seen such question anywhere in any textbook. Any by the way, I know equations related to Fluid mechanics but I'm hopeless here on how to proceed or use the equation.

Textbook style. The wording and layout of the question is exactly what you'd find in a textbook - it doesn't have to be from a textbook, just like it.

A cylindrical tank of radius " r " contains water upto height " H " . There is a hose at height " h " from the bottom. At what angle should the tank be inclined (Of course in the direction of the hose) so as to increase the water output " m " times from the hose?

Inclining the tank is going to have a relatively small effect on increasing flow rate.

Your options are either increase water height (or decrease hose height), or increase hose diameter.

 

[zorro]

A cylindrical tank of radius " r " contains water upto height " H " . There is a hose at height " h " from the bottom. At what angle should the tank be inclined (Of course in the direction of the hose) so as to double the water output from the hose?

N.B. Assume necessary simplifications

I will provide you with some hints -

1) The initial velocity of efflux (v₁) before tilting the tank is very easy to find out. The problem lies in finding out the v.o.e. after tilting the tank. As it depends only on the height of the water level from the orifice (if area of cross section of the hole << area of cross section of the tank), use simple geometry to find it out in terms of the angle rotated. Make an assumption that on tilting the tank, the water doesnot reach the upper end to make calculations easier.

2) Once you get the height, write the expression for the velocity of efflux (v₂) in the second case and use the condition given in the question 2v₁ = v₂.

If you get stuck in any step, show your work till there and I will be glad to help.