Question

Water is flowing in streamline motion through a tube with its axis horizontal. Consider two points A and B in the tube at the same horizontal level.
(a) The pressure in A and B are equal for any shape of the tube.
(b) The pressures are near equal.
(c) The pressures are equal if the tube has a uniform cross-section.
(d) The pressures may be equal if the tube has a non-uniform cross-section.

Answer 1

⭐《ANSWER》

$\huge\mathfrak{\underline {\underline\pink {ANSWER}}}$

↪Actually welcome to the concept of the FLUID MECHANISMS

↪Basically here we are going to discuss the concept of HYDROSTATIC PARADOX

↪Actually according to the hydrostatic paradox , The pressure at point in a liquid is same at the same level , irrespective of the shape of the Container

↪ So , if there are two containers of any shape having same liquid of same density , then according to the BERNOULLIE'S equation , The pressure at same horizontal level in both 11th containers will be same

↪Pressure = rho*g*h

↪So ,

↪a.) THE PRESSURE IN A AND B ARE EQUAL FOR ANY SHAPE OF THE TUBE

Answer 2

Answer ⇒ Option (c). and Option (d).

Explanation ⇒

For Option (c).

Using the Bernoulli's theorem,

P₁ + h₁ρg + 1/2ρv₁² = P₂ + h₂ρg + 1/2ρv₂²

Now, Pipe is horizontal, therefore,

P₁ + 1/2ρv₁² = P₂ +  1/2ρv₂²

  P₁ - P₂ = 1/2 ρ(v₂² - v₁²)

  P₁ - P₂ = ρ(v₂² - v₁²)/2

∴  P₁ - P₂ = (v₂² - v₁²)

Now, P₁ = P₂, only when v₁ = v₂, which will be possible only when, a₁ = a₂.

Hence, option (c). is correct.

''For Option (d). In case of non-uniform cross-section, there are chances (not 100 %), very little, in which area of cross-section many become same. Thus, there velocity will also become same, and hence, Pressure become same, as proved in previous expression''.

I don't think it will now be difficult for you to say, option (a). and (b). is incorrect, becauase area is not same, thus pressure can't be equal.