Flow of Fluid

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JEE Main 2020

A fluid is flowing through a horizontal pipe of varying cross-section with speed $v ms^{- 1}$ at a point where the pressure is $p Pa$ . At another point, where pressure is $\frac{p}{2} Pa$ its speed is $V ms^{- 1}$ . If the density of the fluid is $ρ kg m^{- 3}$ and the flow is streamline, then $V$ is equal to

\frac{p}{ρ} + v

(B)

\frac{2 p}{ρ} + v^{2}

(C)

\frac{p}{2 ρ} + v^{2}

(D)

\frac{p}{ρ} + v^{2}

JEE Main 2020

LEVELJEE Advanced

Water flows in a horizontal tube (see figure). The pressure of water changes by $700 Nm^{- 2}$ between $A$ and $B$ , where the area of cross-section are $40 cm^{2}$ and $20 cm^{2}$ , respectively. Find the rate of flow of water through the tube. (Take, density of water = $1000 kgm^{- 3}$ )

(A)

3020 cm^{3} /s

(B)

2420 cm^{3} /s

(C)

2720 cm^{3} /s

(D)

1810 cm^{3} /s

JEE Main 2019

LEVELJEE Main

Water from a pipe is coming at a rate of $100$ liters per minute. If the radius of the pipe is $5 cm$ , the Reynolds number for the flow is of the order of (density of water = $1000 kg / m^{3}$ , coefficient of viscosity of water = $1 mPa s$ )

(A)

1 0^{3}

(B)

1 0^{4}

(C)

1 0^{2}

(D)

1 0^{6}

JEE Main 2021

LEVELJEE Main

A light cylindrical vessel is kept on a horizontal surface. Area of base is $A$ . A hole of cross-sectional area $a$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is ( $a ≪ A$ ).

(A)

\frac{A}{2 a}

(B)

None of these

(C)

\frac{2 a}{A}

(D)

\frac{a}{A}

JEE Main 2019

LEVELJEE Main

Water flows into a large tank with flat bottom at the rate of $1 0^{- 4} m^{3} s^{- 1}$ . Water is also leaking out of a hole of area $1 cm^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height is

The top of a water tank is open to air and its water level is maintained. It is giving out $0.74 m^{3}$ water per minute through a circular opening of $2 cm$ radius is its wall. The depth of the centre of the opening from the level of water in the tank is close to

(A)

4.8 m

(B)

6.0 m

(C)

2.9 m

(D)

9.6 m

LEVELJEE Main

A cylinder of height $20 m$ is completely filled with water. The velocity of efflux of water (in $ms^{- 1}$ ) through a small hole on the side wall of the cylinder near its bottom, is

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4 cm$ and $4.8 cm$ , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

(A)

\frac{9}{16}

(B)

\frac{81}{256}

(C)

\frac{3}{2}

(D)

\frac{3}{4}

JEE Main 2021

LEVELJEE Advanced

Consider a water tank as shown in the figure. It's cross-sectional area is $0.4 m^{2}$ . The tank has an opening $B$ near the bottom whose cross-section area is $1 cm^{2}$ . A load of $24 kg$ is applied on the water at the top when the height of the water level is $40 cm$ above the bottom, the velocity of water coming out the opening $B$ is $v ms^{- 1}$ . The value of $v$ , to the nearest integer, is ............... . (Take value of $g$ to be $10 ms^{- 2}$ )

JEE Main 2019

LEVELJEE Advanced

A liquid of density $ρ$ is coming out of a hose pipe of radius $a$ with horizontal speed $v$ and hits a mesh. 50\% of the liquid passes through the mesh unaffected 25\% losses all of its momentum and, 25\% comes back with the same speed. The resultant pressure on the mesh will be

(A)

ρ v^{2}

(B)

\frac{1}{2} ρ v^{2}

(C)

\frac{1}{4} ρ v^{2}

(D)

\frac{3}{4} ρ v^{2}

JEE Main 2021

LEVELJEE Main

The water is filled upto height of $12 m$ in a tank having vertical sidewalls. A hole is made in one of the walls at a depth $h$ below the water level. The value of $h$ for which the emerging stream of water strikes the ground at the maximum range is ...... m.

JEE Main 2019

LEVELJEE Main

Water from a tap emerges vertically downwards with an initial speed of $1.0 ms^{- 1}$ . The cross-sectional area of the tap is $1 0^{- 4} m^{2}$ . Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, $0.15 m$ below the tap would be [Take, $g = 10 ms^{- 2}$ ]

(A)

2 \times 1 0^{- 5} m^{2}

(B)

1 \times 1 0^{- 5} m^{2}

(C)

5 \times 1 0^{- 4} m^{2}

(D)

5 \times 1 0^{- 5} m^{2}

JEE Main 2021

LEVELJEE Main

What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18 L/min$ to $0.48 L/min$ ? The radius of the tap and viscosity of water are $0.5 cm$ and $1 0^{- 3} Pa-s$ , respectively. (Density of water = $1 0^{3} kg/m^{3}$ )

(A)

Unsteady to steady flow

(B)

Remains steady flow

(C)

Remains turbulent flow

(D)

Steady flow to unsteady flow

LEVELJEE Advanced

Water is flowing continuously from a tap having an internal diameter $8 \times 1 0^{- 3} m$ . The water velocity as it leaves the tap is $0.4 ms^{- 1}$ . The diameter of the water stream at a distance $2 \times 1 0^{- 1} m$ below the tap is close to

(A)

7.5 \times 1 0^{- 3} m

(B)

9.6 \times 1 0^{- 3} m

(C)

3.6 \times 1 0^{- 3} m

(D)

5.0 \times 1 0^{- 3} m

JEE Advanced 1997

LEVELJEE Advanced

A large open top container of negligible mass and uniform cross-sectional area $A$ has a small hole of cross-sectional area $A /100$ in its side wall near the bottom. The container is kept on a smooth horizontal floor and contains a liquid of density $ρ$ and mass $m_{0}$ . Assuming that the liquid starts flowing out horizontally through the hole at $t = 0$ . Calculate (a) the acceleration of the container and (b) velocity of efflux when 75% of the liquid has drained out.

JEE Advanced (2000)

LEVELJEE Main

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4 y$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, $R$ is equal to

(A)

\frac{L}{2 π}

(B)

2 π L

(C)

L

(D)

\frac{L}{2 π}

JEE Advanced 1997

LEVELJEE Main

A non-viscous liquid of constant density $1000 kg/m^{3}$ flows in streamline motion along a tube of variable cross-section. The tube is kept inclined in the vertical plane as shown in the figure. The area of cross-section of the tube at two points P and Q at heights of $2 m$ and $5 m$ are respectively $4 \times 1 0^{- 3} m^{2}$ and $8 \times 1 0^{- 3} m^{2}$ . The velocity of the liquid at point P is $1 m/s$ . Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point P to Q.

JEE Advanced 2008

LEVELJEE Main

Assertion: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. Reason: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

(A)

If Assertion is true, Reason is true; Reason is the correct explanation for Assertion

(B)

If Assertion is true, Reason is true; Reason is not a correct explanation for Assertion

(C)

If Assertion is true; Reason is false

(D)

If Assertion is false; Reason is true

JEE Advanced 1994

LEVELJEE Main

A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross-sectional area is $10 cm^{2}$ , the water velocity is $1 ms^{- 1}$ and the pressure is $2000 Pa$ . The pressure of water at another point where the cross-sectional area is $5 cm^{2}$ , is ......Pa. (Density of water = $1 0^{3} kg-m^{- 3}$ )

JEE Advanced 2005

LEVELJEE Main

Water is filled in a cylindrical container to a height of $3 m$ . The ratio of the cross-sectional area of the orifice and the beaker is $0.1$ . The square of the speed of the liquid coming out from the orifice is ( $g = 10 m/s^{2}$ )

(A)

50 m^{2} / s^{2}

(B)

50.5 m^{2} / s^{2}

(C)

51 m^{2} / s^{2}

(D)

52 m^{2} / s^{2}

JEE Advanced 2014

LEVELJEE Main

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance $d$ of $1.2 m$ from the person. In the following, state of the lift’s motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the code given below the lists. \begin{array}{l|l} \hline \textbf{List I} & \textbf{List II} \\ \hline \text{A. Lift is accelerating vertically up.} & \text{p. } d = 1.2\text{ m} \\ \text{B. Lift is accelerating vertically down with an acceleration less than } g. & \text{q. } d > 1.2\text{ m} \\ \text{C. Lift is moving vertically up with constant speed.} & \text{r. } d < 1.2\text{ m} \\ \text{D. Lift is falling freely.} & \text{s. No water leaks out of the jar} \\ \hline \end{array}

Consider a horizontally oriented syringe containing water located at a height of $1.25 m$ above the ground. The diameter of the plunger is $8 mm$ and the diameter of the nozzle is $2 mm$ . The plunger is pushed with a constant speed of $0.25 m/s$ . Find the horizontal range of water stream on the ground. (Take $g = 10 m/s^{2}$ ).

JEE Advanced 1998

LEVELJEE Main

Water from a tap emerges vertically downwards with an initial speed of $1.0 m/s$ . The cross-sectional area of tap is $1 0^{- 4} m^{2}$ . Assume that the pressure is constant throughout the stream of water and that the flow is steady, the cross-sectional area of stream $0.15 m$ below the tap is

(A)

5.0 \times 1 0^{- 4} m^{2}

(B)

1.0 \times 1 0^{- 4} m^{2}

(C)

5.0 \times 1 0^{- 5} m^{2}

(D)

2.0 \times 1 0^{- 5} m^{2}

JEE Advanced 2024

LEVELJEE Advanced

Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height h in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are $t_{1}$ and $t_{2}$ , respectively. If $H = (\frac{16}{9}) h$ , then the ratio $t_{1} / t_{2}$ is________.

JEE Advanced 2026

LEVELJEE Advanced

Comprehension Passage

A container of height

2 m

, length

2 m

and breadth

1 m

is made of insulating vertical walls and two large area horizontal metal plates (

M_{1}

and

M_{2}

) which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area

10 cm^{2}

near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant

ϵ_{r} = 15

and the right chamber is empty (

ϵ_{r} = 1

). At time

t = 0

, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has

ϵ_{r} = 1

and is maintained at atmospheric pressure. The schematic of the container at a time

t > 0

is shown in the figure. [Given: acceleration due to gravity is

10 ms^{- 2}

Question 1:

The height (in m) of the liquid in left chamber at $t = 500 s$ is :

Question 2:

The difference in the capacitance (in F) between the metal plates at $t = 0$ and that at $t = 500 s$ is $(8 - n) ϵ_{0}$ , where $ϵ_{0}$ is the permittivity of free space. The value of $n$ is :

Assertion: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. Reason: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The height (in m) of the liquid in left chamber at t=500 s is :

The height (in m) of the liquid in left chamber at $t = 500 s$ is :