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A container of large uniform cross-sectional area A resting on a horizontal surface has two immiscible, non-viscous and incompressible liquids of densities d and 2d, each of height H/2 as shown. The lower density liquid is open to the atmosphere having pressure P0. A tiny hole of area s(s<<A) is punched on the vertical side of the container at a height h (h < H/2). Determine: 
  • a)
    The initial speed of efflux of the liquid at the hole is 
  • b)
    The horizontal distance x travelled by the liquid initially is 
  • c)
    The height hm at which the hole should be punched so that the liquid travels the maximum distance xm initially is 0.75H
  • d)
    None of these
Correct answer is option 'A,B,C'. Can you explain this answer?
Verified Answer
A container of large uniform cross-sectional area A resting on a horiz...
Here the effective height of orifice cannot be taken as (H-h) due to the presence of two liquids. Using Berrnoulli,s theorem just inside and just outside the orifice, we have


where V is the velocity of efflux


...(i)
2. Let be the time taken by the liquid to hit the ground. Then
....(ii)
The horizontal range x = Vt
 [use equation (1) and (2)]

...(iii)
3. Q 
Differentiate x with respect to h and equate it to zero for maximum h.



Value of h put in equation(3)

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Most Upvoted Answer
A container of large uniform cross-sectional area A resting on a horiz...
Here the effective height of orifice cannot be taken as (H-h) due to the presence of two liquids. Using Berrnoulli,s theorem just inside and just outside the orifice, we have


where V is the velocity of efflux


...(i)
2. Let be the time taken by the liquid to hit the ground. Then
....(ii)
The horizontal range x = Vt
 [use equation (1) and (2)]

...(iii)
3. Q 
Differentiate x with respect to h and equate it to zero for maximum h.



Value of h put in equation(3)

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A container of large uniform cross-sectional area A resting on a horizontal surface has two immiscible, non-viscous and incompressible liquids of densities d and 2d, each of height H/2 as shown. The lower density liquid is open to the atmosphere having pressure P0. A tiny hole of area s(s<<A) is punched on the vertical side of the container at a height h (h < H/2). Determine:a)The initial speed of efflux of the liquid at the hole isb)The horizontal distance x travelled by the liquid initially isc)The height hm at which the hole should be punched so that the liquid travels the maximum distance xm initially is 0.75Hd)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer?
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