Bernoulli's principle and its applications — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For steady flow of an incompressible, non-viscous fluid along a streamline, which expression remains constant according to Bernoulli's principle?

• A. $P + \frac{1}{2}\rho v^2 + \rho gh$
• B. $P + \rho v^2 + \rho gh$
• C. $P - \frac{1}{2}\rho v^2 + \rho gh$
• D. $P + \rho gh$

Question 2 · difficulty L2 · understanding

Water flows steadily through a horizontal pipe that becomes narrower. Which change occurs as the water enters the narrower section?

• A. Speed decreases and pressure increases
• B. Speed increases and pressure decreases
• C. Both speed and pressure increase
• D. Both speed and pressure remain unchanged

Question 3 · difficulty L2 · understanding

A small hole is made in the side of a large open tank at a depth $h$ below the water surface. Neglecting viscosity, what happens to the speed of efflux if the depth of the hole is increased from $h$ to $4h$?

• A. It becomes four times
• B. It becomes twice
• C. It becomes one-half
• D. It remains unchanged

Question 4 · difficulty L2 · understanding

In a perfume atomizer, fast-moving air is blown across the mouth of a vertical tube dipping into the liquid. Why does the liquid rise in the tube?

• A. The fast air increases the pressure above the tube and pushes the liquid downward
• B. The fast air lowers the pressure at the tube mouth, so the higher pressure on the liquid surface pushes the liquid upward
• C. The liquid rises because its density decreases when air moves over it
• D. The moving air pulls the liquid upward only by viscous friction

Question 5 · difficulty L3 · application

Water flows through a horizontal pipe. At section 1, the cross-sectional area is $4\,\text{cm}^2$, the speed is $2\,\text{m s}^{-1}$ and the pressure is $1.50\times10^5\,\text{Pa}$. At section 2, the area is $2\,\text{cm}^2$. Taking the density of water as $1000\,\text{kg m}^{-3}$, what is the pressure at section 2?

• A. $1.38\times10^5\,\text{Pa}$
• B. $1.44\times10^5\,\text{Pa}$
• C. $1.49\times10^5\,\text{Pa}$
• D. $1.56\times10^5\,\text{Pa}$

Question 6 · difficulty L3 · application

A large open tank contains water. A small hole is located $5\,\text{m}$ below the free surface. Neglecting viscosity and taking $g=10\,\text{m s}^{-2}$, what is the speed of water emerging from the hole?

• A. $5\,\text{m s}^{-1}$
• B. $10\,\text{m s}^{-1}$
• C. $25\,\text{m s}^{-1}$
• D. $100\,\text{m s}^{-1}$

Question 7 · difficulty L3 · application

A horizontal Venturi tube carries water. The diameters of its wider and narrower sections are $4\,\text{cm}$ and $2\,\text{cm}$ respectively. If the speed in the wider section is $1\,\text{m s}^{-1}$, what is the pressure difference between the wider and narrower sections? Take $\rho=1000\,\text{kg m}^{-3}$.

• A. $1.5\,\text{kPa}$
• B. $7.5\,\text{kPa}$
• C. $15\,\text{kPa}$
• D. $30\,\text{kPa}$

Question 8 · difficulty L3 · application

A Pitot tube measures the speed of air. The stagnation pressure exceeds the static pressure by $800\,\text{Pa}$. If the air density is $1.25\,\text{kg m}^{-3}$, what is the air speed?

• A. $25\,\text{m s}^{-1}$
• B. $36\,\text{m s}^{-1}$
• C. $45\,\text{m s}^{-1}$
• D. $1280\,\text{m s}^{-1}$

Question 9 · difficulty L4 · application

Water flows steadily upward through a pipe. At a lower section, the area is $A$, speed is $3\,\text{m s}^{-1}$ and pressure is $2.50\times10^5\,\text{Pa}$. At a point $4\,\text{m}$ higher, the area is $A/2$. Taking $\rho=1000\,\text{kg m}^{-3}$ and $g=10\,\text{m s}^{-2}$, what is the pressure at the upper point?

• A. $1.965\times10^5\,\text{Pa}$
• B. $2.235\times10^5\,\text{Pa}$
• C. $2.10\times10^5\,\text{Pa}$
• D. $2.365\times10^5\,\text{Pa}$

Question 10 · difficulty L4 · application

The water surface in a large tank is $20\,\text{m}$ above the ground. A small hole in the vertical side ejects water horizontally. At what height above the ground should the hole be made so that the horizontal range of the water jet is maximum?

• A. $5\,\text{m}$
• B. $10\,\text{m}$
• C. $15\,\text{m}$
• D. $20\,\text{m}$