(it also had a figure but i Can't upload it )

Q 1.316     Two manometric tubes are mounted on a horizontal pipe of varying cross section at S₁ and S₂  find the volume of water flowing across the pipe's section per unit time if the diffrence in water columns is equal to .

Is the answer.

applying bernouli's theoram for water flow thru' the 2 surfaces S₁ and S₂.......

P₁+ hdg  + 1/2dv₁² = P₂+ hdg  + 1/2dv₂²............where h= the height from the, the two surfaces are located....

P₁=P + H₁dg........and P₂=P + H₂dg.......P=atmospheric pressure...

applying we have dH g = 1/2(v₂²-v₁²)

but we have from eqn. of continuity S₁v₁=S₂v₂

applying this we have SV =

rate if useful......

my solution. Didn't had time so posting later.

From the conservation of mass

.............(1)

But as shown in the figure. Therefore,

As every steamline is horizontal between 1 & 2, Bernoull's theorm becomes

= constant which gives as

As the difference in height of water column is , therefore .......(2)

From Bernoull's theorm between points 1 and 2 of a streamline

or .............(3)

Using (1) in (3), we get 

Hence

Rate  if helpful.