Equation of Continuity

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

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.

State properties of an ideal fluid. 

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

(Take $\sqrt{2}=1.4$)

In the given figure, the velocity $v_3$ ( in $\mathrm{m} {\mathrm{s}}^{-1}$) will be

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 $2 \mathrm{m}/\mathrm{s}$, $4 \mathrm{m}/\mathrm{s}$, and $4 \mathrm{m}/\mathrm{s}$ respectively, the velocity of the fluid at $D$ (in m/s) is -

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?

A horizontal pipe has a cross-section of $10$ ${\mathrm{cm}}^2$ in one region and of $5$ ${\mathrm{cm}}^2$ in another. The water velocity at the first is $5 \mathrm{m} {\mathrm{s}}^{-1}$ and the pressure in the second is $2\times {10}^5$. The pressure of water in $1^{st}$ region is given by $237.5\times {10}^{\mathrm{\alpha }} \mathrm{Pa}$. Then the value of $\alpha$ is.

List the properties of ideal fluids?

If the velocity head of a stream of water is equal to $10 \mathrm{cm}$, then its speed of flow is approximately

A portion of a tube is shown in the figure. Fluid is flowing from cross-section area $A_1$ to $A_2$. The two cross-sections are at distance$।$ from each other. The velocity of the fluid at section $A_2$ is $\sqrt{\frac{g\ell }{2}}$. If the pressures at $A_1 \& A_2$ are same, then the angle made by the tube with the horizontal will be

A horizontal pipe has a cross-section of $10$ ${\mathrm{cm}}^2$ in one region and of $5$ ${\mathrm{cm}}^2$ in another. The water velocity at the first is $5 \mathrm{m} {\mathrm{s}}^{-1}$ and the pressure in the second is $2\times {10}^5$. The pressure of water in $1^{st}$ region is given by $237.5\times {10}^{\mathrm{\alpha }} \mathrm{Pa}$. Then the value of $\alpha$ is.

Water is moving with a speed of $5.18 \mathrm{m} {\mathrm{s}}^{-1}$ through a pipe with a cross-sectional area of $4.20 {\mathrm{cm}}^2$. The water gradually descends $9.66 \mathrm{m}$ as the pipe increases in area to $7.60 {\mathrm{cm}}^2$. The speed of flow at the lower level is

Statement 1: A water stream falls from a tap becomes narrower as it falls.

Statement 2: The velocity of water increases as it falls.

Water is flowing through a channel of width $12\mathrm{ }\mathrm{m}$ with a speed of $0.75\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. The water then flows into four identical channels of width of $4 \mathrm{m}$ each. The depth of the water does not change as it flows into the four identical channels. Find the speed of the water in one of the smaller channel?

Blood is flow rate through a capillary of cross-sectional area of  $0.25\mathrm{ }{\mathrm{m}}^2$ is $100\mathrm{ }{\mathrm{c}\mathrm{m}}^3 {\mathrm{s}}^{-1}$$$. The velocity of flow of blood is -

A glass tube has three different cross sectional areas with the values indicated in the figure. A piston at the left end of the tube exerts pressure so that the mercury within the tube flows from the right end with a speed of $8.0\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. Three points within the tube are labeled $A, B$ and $C$. The atmospheric pressure is $1.01\times {10}^5\mathrm{ }\mathrm{N} {\mathrm{m}}^{-2}$; and the density of mercury is $1.36\times {10}^4\mathrm{ }\mathrm{kg} {\mathrm{m}}^{-2}$ (use $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$):

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?

The small orifice between two communicating vessels have area $1$ sq. cm. The surface area of the horizontal sections of the first and the second vessel are $10 {\mathrm{m}}^2$ and $5 {\mathrm{m}}^2$ respectively. Initially the level of liquid in the first and second vessel is $15 \mathrm{m}$ and $5 \mathrm{m}$ from the orifice. Given that velocity of liquid flow is $v=\sigma \sqrt{2g\left(h_1-h_2\right)}$ m/s, where h₁ and h₂ is the height of liquid in the two vessels, then the time required for the liquid to reach the same level is $\frac{10^t}{15\sigma \sqrt{20g}}$, where t is equal to

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 $2 \mathrm{m}/\mathrm{s}$, $4 \mathrm{m}/\mathrm{s}$, and $4 \mathrm{m}/\mathrm{s}$ respectively, the velocity of the fluid at $D$ (in m/s) is $\sqrt{x}$. Find the value of $x$