Equation of Continuity

IMPORTANT

Equation of Continuity: Overview

This topic covers concepts, such as, Equation of Continuity etc.

Important Questions on Equation of Continuity

HARD
IMPORTANT

A laminar stream is flowing vertically down from a tap of cross-section area 1 cm2. At a distance 10 below the tap, the cross-section area of the stream has reduced to 1/2 cm​2. Find the volumetric flow rate of water from the tap

MEDIUM
IMPORTANT

A cylindrical vessel open at the top is 20 cm high and 10 cm in diameter. A circular hole whose cross-sectional area 1cm2 is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate 100 cm3 s​-1 . Find the height of water in the vessel under steady state.

MEDIUM
IMPORTANT

Water from a tap emerges vertically downwards with an initial speed of  1.0 ms-1 . The cross - sectional area of the tap is  10-4 m2 . 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 )

MEDIUM
IMPORTANT

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum din meters 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:

MEDIUM
IMPORTANT

Water from a tap emerges vertically downwards with an initial speed of 1.0 m s-1. The cross -sectional area of the tap is  10-4 m2 . 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 m s-2 )

EASY
IMPORTANT

Water is moving with a speed of 5.18 m s-1 through a pipe with a cross-sectional area of 4.20 cm2. The water gradually descends 9.66 m as the pipe increases in area to 7.60 cm2. The speed of flow at the lower level is

MEDIUM
IMPORTANT

Water is flowing at a speed of 1.5 m s-1 through a horizontal tube of cross-sectional area 10-2 m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water =103 kg m-3)

HARD
IMPORTANT

If the velocity head of a stream of water is equal to 10 cm, then its speed of flow is approximately ( in m/s)

(Take 2=1.4)

EASY
IMPORTANT

In the given figure, the velocity v3 ( in m s-1) will be

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EASY
IMPORTANT

An ideal fluid is flowing in two pipes of the same cross-sectional pipe area. Both the pipes are connected with two vertical tubes, of length h1 and h2 as shown in the figure. The flow is streamline in both pipes. If the velocity of the fluid at A, B, and C are 2 m/s, 4 m/s, and 4 m/s respectively, the velocity of the fluid at D (in m/s) is -
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HARD
IMPORTANT

The cylindrical tube of a spray pump has a cross-section of 8.0 cm2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m/min, what is the speed of ejection of the liquid through the holes?

EASY
IMPORTANT

A horizontal pipe has a cross-section of 10 cm2 in one region and of 5 cm2 in another. The water velocity at the first is 5 m s1 and the pressure in the second is 2×105. The pressure of water in 1 st region is given by 237.5×10α Pa. Then the value of α is.

HARD
IMPORTANT

If the velocity head of a stream of water is equal to 10 cm, then its speed of flow is approximately

HARD
IMPORTANT

A portion of a tube is shown in the figure. Fluid is flowing from cross-section area A1 to A2. The two cross-sections are at distance  from each other. The velocity of the fluid at section A2 is g2. If the pressures at A1 & A2 are same, then the angle made by the tube with the horizontal will be

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HARD
IMPORTANT

Mumbai needs 1.4×1012 L of water annually. Its effective surface area is 600 km2 and it receives an average rainfall of 2.4 m annually. If 10% of this rain water is conserved, it will meet approximately

EASY
IMPORTANT

The pipe shows the volume flow rate of an ideal liquid at a certain time and its direction. What is the value of Q in m3/s (Assume steady-state and equal area of cross-section at each opening)

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EASY
IMPORTANT

An incompressible liquid is flowing through a horizontal pipe as shown in figure. The value of speed v is (areas are indicated in figure)

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HARD
IMPORTANT

A vessel of area of cross-section A has liquid to a height H.There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from H1 toH2 will be (a <<A) :

MEDIUM
IMPORTANT

Calculate the ratio of speed, if the radii of the ends of a conical section of pipe are 0.1 m and 0.04 m is

EASY
IMPORTANT

The total area of cross-section is 0.25 m2. If the blood is flowing at the rate of 100 cm3/sec, then the average velocity of flow of blood through the capillaries is :