Q 1 :    

An ideal fluid is flowing in a non-uniform cross-sectional tube XY (as shown in the figure) from end X to end Y. If K1 and K2 are the kinetic energy per unit volume of the fluid at X and Y respectively, then the correct option is                 [2024]

[IMAGE 94]
 

  • K1=K2

     

  • 2K1=K2

     

  • K1>K2

     

  • K1<K2

     

(3)

The cross-section area of X is smaller than the Y.

Using equation of continuity for ideal fluid, a1v1=a2v2  

v1>v2                                                                    (a1<a2)

So, the K.E.Volume of x(K1)>K.E.Volume of y(K2)  

     K1>K2                                                     (K=12ρv2)



Q 2 :    

The venturi-meter works on                        [2023]

  • the principle of parallel axes

     

  • the principle of perpendicular axes

     

  • Huygen’s principle

     

  • Bernoulli’s principle

     

(4)

Venturimeter is a device which is used for measuring the rate of flow of fluids. It works on Bernoulli’s principle.

 



Q 3 :    

A small hole of area of cross-section 2 mm2 is present near the bottom of a fully filled open tank of height 2 m. Taking g=10 m/s2, the rate of flow of water through the open hole would be nearly              [2019]
 

  • 6.4×10-6 m3/s

     

  • 12.6×10-6 m3/s

     

  • 8.9×10-6 m3/s

     

  • 2.23×10-6 m3/s

     

(2)

According to Torricelli's theorem,

Velocity, v=2gh=2×10×2=6.32 m/s.

From equation of continuity, 

Volume of liquid flowing per second, Q=Av

=2×10-6×6.32=12.6×10-6 m3/s



Q 4 :    

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be (ρair=1.2kg/m3)                      [2015]
 

  • 2.4×105N, upwards

     

  • 2.4×105N, downwards

     

  • 4.8×105N, downwards

     

  • 4.8×105N, upwards

     

(1)