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What are the assumptions used for deriving Bernoulli's equation?

Important Questions on Mechanical Properties of Fluids

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A fluid is flowing through a horizontal pipe of varying cross-section, with

v {ms}^{- 1}

at a point where the pressure is

P

Pascal. At another point where pressure

\frac{P}{2}

Pascal 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

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

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In the diagram shown, the difference in the two tubes of the manometer is $5 cm$ , the cross-section of the tube at $A$ and $B$ is $6 {mm}^{2}$ and $10 {mm}^{2}$ respectively. The rate at which water flows through the tube is $(g = 10 m s^{- 2})$

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A cylindrical container containing water has a small hole at height of $H = 8 cm$ from the bottom and at a depth of $2 cm$ from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground $(x)$ is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A small hole of area cross-section

2 m m^{2}

is present near the bottom of a fully filled open tank of height

2 m .

Taking

g = 10 m s^{- 2}

, the rate of flow of water through the open hole would be nearly

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

Water flows into a large tank with flat bottom at the rate of

10^{- 4} m^{3} s^{- 1} .

Water is also leaking out of a hole of area

1 c m^{2}

at its bottom. If the height of the water in the tank remains steady then this height is:

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

Figures below show water flowing through a horizontal pipe from left to right. Note that the pipe in the middle is narrower. Choose the most appropriate depiction of water levels in the vertical pipes.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r

(r < < R)

at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then:

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

An ideal liquid flows through a horizontal tube of variable diameter. The pressure is lowest where the _____.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

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 in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A wind with speed

40 m s^{- 1}

blows parallel to the roof of a house. The area of the roof is

250 m^{2}

. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the direction of the force will be :

(ρ_{air} = 1.2 kg m^{- 3})

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

Bernoulli's theorem is based on the principle of conservation of

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density

d

. The area of the base of both vessels is

S

but the height of liquid in one vessel is

x_{1}

and in the other

x_{2}

. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is :

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A light cylindrical vessel is kept on a horizontal surface. Area of the 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

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A cylindrical tank with a large diameter is filled with water. Water drains out through a hole at a bottom of the tank. If the cross-sectional area of the hole is

6 {cm}^{2}

then the drainage rate

(m^{3} s^{- 1})

when the depth of the water is

0.2 m

, is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A cylindrical vessel of radius

5 cm

is filled with water up to a height of

20 cm

. The cylinder is open to atmosphere at the top. A small aperture of radius

2 mm

is made on the side of the cylinder at a height of

5 cm

from the bottom of the vessel. For approximately how long will water leak out of the aperture?

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

A wind with a speed

40 m \cdot s^{- 1}

blows parallel to the roof of a house. Area of the roof is

250 m^{2} .

Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and direction of the force will be _________

(ρ_{air} = 1.2 kg \cdot m^{- 3})

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

Assertion (A): The upper surface of the wing of an aeroplane is made convex and the lower surface is made concave.
Reason (R): The air currents at the top have smaller velocity and thus less pressure at the bottom than at the top.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Bernoulli's Principle and its Applications

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of the water is