What Determines the Pressure at Mid-Point in a Siphon Tube?

[utkarshakash]

Homework Statement

A wide vessel and a tube is connected as shown in the figure(see attachment). Water is filled inside vessel and tube. When tube is opened the water flows out as shown in the figure. The pressure at point P,at mid-point of the tube is (cross-section of the tube is very very small)

Homework Equations

Bernoulli Equation
Equation of Continuity

The Attempt at a Solution

Applying Bernoulli's Equation at the top of vessel and at point P and assuming datum level to be the base of the vessel

$P_o + \rho gH+\frac{1}{2} \rho v_1 ^2 = P_p + \frac{1}{2}\rho v_2 ^2 + \rho g (-H)$

Assuming area of cross section of vessel and tube be A and a and applying eqn of continuity

$Av_1 = av_2$

Substituting value of v1 in prev eqn

$P_o + \rho gH+\frac{1}{2} \rho \dfrac{a^2 v_2 ^2}{A^2} = P_p + \frac{1}{2}\rho v_2 ^2 + \rho g (-H)$

Now there comes another unknown variable v2 the value of which is unknown to me :(

 

[DeShark]

You might want to consider this as a simple siphon, and given the wording of the question, you should take the first flow rate to be zero. V1 = 0. You know the height between the surface of the water and the exit point, the density of water, atmospheric pressure, etc. The pressure at the exit is atmospheric also.

So you calculate v2 from that. Once you have v2, you can use the equation of continuity to get the velocity at point P (hint: it's super easy 'cause water is incompressible). Then you can work out what the pressure is at point P from there.

http://en.wikipedia.org/wiki/Siphon#Velocity

 

[utkarshakash]

You might want to consider this as a simple siphon, and given the wording of the question, you should take the first flow rate to be zero. V1 = 0. You know the height between the surface of the water and the exit point, the density of water, atmospheric pressure, etc. The pressure at the exit is atmospheric also.

So you calculate v2 from that. Once you have v2, you can use the equation of continuity to get the velocity at point P (hint: it's super easy 'cause water is incompressible). Then you can work out what the pressure is at point P from there.

http://en.wikipedia.org/wiki/Siphon#Velocity

Cool! That worked. Thanks for your help.