Test: Pressure, Streamline flow & Bernoulli's Principle (21 August) - JEE MCQ

Pressure of 1 atm = 1.013 x 10⁵ Pa

Pascal's law states that the magnitude of pressure within the fluid is equal in all parts.

Option A: Brahma's press is a Hydraulic Press that works on the principle of Pascal's law.

Option B: Submarines don't work on the principle of Pascal's law.

Option C: Hydraulic lifts works on the principle of pascals law i.e. a force applied on a smaller cylinder is transmitted to lift heavy loads using larger cylinders.

Hence, option B is correct.

Pressure at the bottom of a tank containing liquid is given as P = hρg which is independent of the surface area bottom of the tank.

► Pressure = Density x Gravity x Height = ρgh 
⇒  ρ = P/(g*h) = 80 Pa / (9.8 m/s² x 5 m)
⇒ Density = 1.632 kg/m³

Bernoulli’s theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli’s theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow and is the basis for many engineering applications.

Applying Bernoulli's principle, we have
P₁+1/2​ρv₁²=P₂+1/2​ρv₂² 
⇒P₂​−P₁=1/2ρ (v2/1−v2/2)
⇒ΔP=1/2​×1.3× (1202−90²)
⇒ΔP=0.65× (120+90) × (120−90)
⇒ΔP=0.65×210×30=4095Pa

Every foot of elevation change causes a 0.433 PSI change in water pressure. If your pipe is going downhill add 0.433 PSI of pressure per vertical foot the pipe goes down. If the pipe is going uphill subtract 0.433 PSI for every vertical foot the pipe goes up.

In streamline flow, the product of cross section area and velocity remains constant (equation of continuity). So in the narrowest part of the pipe velocity is maximum. 
And from Bernoulli's theorem, we know that the sum of potential energy, kinetic energy and pressure energy remains constant. Since pipe is horizontal potential energy is equal at all the points. So the narrowest part  of pipe pressure (pressure energy) will be minimum because velocity (kinetic energy) is maximum in the narrowest part.

Bernoulli's principle can even be derived from the principle of conservation of energy. Bernoulli's principle states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline.
Hence D is the correct answer.