Question

A non-viscous liquid of constant density 1000 kg/m3 flows in a streamline motion along a tube of variable cross-section. The tube is kept inclined in the vertical plane as shown in figure. The area of cross-section of the tube at two points P and Q at heights of 2 metre and 5 metre are respectively  the velocity of the liquid at point P is 1 m/s. Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point P to Q.     

                                                          

Solution

Correct option is

29025 J

 

As gravitational field is conservative, i.e., W = –U  

  

                   

                     

So work done by the force of gravity per unit volume            

        

                    

Now in case of ideal fluid motion by conservation of mass, i.e.,

        

  

                           

Now as work done per unit volume by pressure, 

         

But by Bernoulli’s theorem, 

         

  

which in the light of eq. (i) and (ii) yields  

        

SIMILAR QUESTIONS

Q1

To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid passes on the side of the vessel equal to the force exerted be the liquid on the bottom of the vessel?

Q2

 

The density of air in atmosphere decreases with height and can be expressed by the relation:  

           

Where  is the density at sea-level, A is a constant and h is the height. Calculate the atmospheric pressure at sea-level. Assume g to be constant. 

Q3

 

A rod of length 6 m has a mass 12 kg. It is hinged at one end at a distance of 3 m below water surface. (a) What weight must be attached to the other end of the rod so that 5 m of the rod are submerged? (b) Find the magnitude and direction of the force exerted by the hinge on the rod. 

(Specific gravity of rod is 0.5).

Q4

 

A large block of ice 5 m thick has a vertical hole drilled through it floating in the middle of a lake. What is the minimum length of a rope required to scoop up a bucket full of water through the hole?

[RD of ice = 0.9]

                                                                              

Q5

 

A cubical block of iron 5 cm on each side is floating on mercury in a vessel. Water is poured into the vessel so that it just covers the iron block. What is the height of water column? 

[RD of Hg = 13.6 and Fe = 7.2] 

Q6

A glass beaker having mass 390 g and an interior volume of 500 cm3 floats on water when it is less than half filled with water. What is the density of the material of the beaker?

Q7

 

A block of wood weighs 12 kg and has a relative density 0.6. It is to be in water with 0.9 of its volume immersed. What weight of a metal is needed if the metal is attached below the wood?

[RD of metal = 14]  

Q8

A wooden stick of length L, radius R and density  has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value of the mass m (in terms of given parameters) that would make the stick float vertically in equilibrium in a liquid of density 

Q9

Calculate the rate of flow of glycerine of density  through the conical section of a pipe, if the radii of its ends are 0.1 m and 0.04 m and the pressure drop across its length is 10 N/m2.

Q10

The fresh water behind a reservoir dam is 15 m deep. A horizontal pipe 4.0 cm in diameter passes through the dam 6.0 m below the water surface as shown in figure. A plug secures the pipe opening. The plug is removed. What volume of water flows out of the pipe in 3.0- hour?