Bernoulli's Equation

An incompressible fluid (ideal fluid) is flowing through non uniform cross-sectional tube PQ as shown in the figure from end P to end Q. If $K_P$ and $K_Q$ are the kinetic energy per unit volume of the fluid at end P and end Q respectively, then

A horizontal pipe carries water in a streamline flow. At point along the pipe, where the cross- sectional area is $A_1$, the velocity of water is $V_1$ and the pressure is $P_1$. What is the pressure of water at another point where the cross-sectional area is $A_2$?

A closed pipe containing liquid showed a pressure $P_1$ by gauge. When the valve was opened, pressure was reduced to $P_2$. The speed of water flowing out of the pipe is ($\rho$=density of water)

Water flows in a streamline motion through a horizontal pipe of circular cross-section as shown in the figure. The pressure difference of water between $P$ and $Q$ is $15\text{ Nm}^{-2}$. The area of cross-section at $P$ and $Q$ are $40\text{ cm}^2$ and $20\text{ cm}^2$, respectively. The rate of flow of water through the pipe, in $\text{cm}^3\text{ s}^{-1}$, is:

[Take density of water $= 1000\text{ kg m}^{-3}$ ]

A liquid of density $600\text{ kg/m}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0\text{ cm}^2$ and that at $B$ is $20\text{ mm}^2$. Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is $10\text{ cm/s}$. The difference in pressures at $A$ and $B$ points is ______ Pa.

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at $A$ and $B$ are $6\text{ cm}^2$ and $3\text{ cm}^2$ respectively. The rate of flow will be $\underline{\hspace{3em}}\ \text{cm}^3/\text{s}$. (take $g = 10\text{ m/s}^2$)

A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross- sectional area is $10\text{ cm}^2$, the velocity of water is $1\text{ m/s}$ and pressure is 2000 Pa. The pressure of water at another point where the cross-sectional area $5\text{ cm}^2$ is

[Given $\rightarrow$ density of water $= 1000\text{ kg/m}^3$ ]

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

A tube of length $L$ is shown in the figure. The radius of cross section at the point $(1)$ is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is $2\text{ m/s}$, then velocity of water leaving the point (2) will be

Correct Bernoulli's equation is (symbols have their usual meaning):

A closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened, pressure was reduced to $P_2$. The speed of water flowing out of the pipe is ($\rho =$ density of water)

Water is flowing in a conical tube as shown in figure. Velocity of water at area ' $A_2$ ' is $60\text{ cm/s}$. The value of ' $A_1$ ' and ' $A_2$ ' is $10\text{ cm}^2$ and $5\text{ cm}^2$ respectively. The pressure difference at both the cross- section is

A streamline flow of a liquid of density ' $\rho$ ' is passing through a horizontal pipe of crosssectional area $A_1$ and $A_2$ at two ends. If the pressure of liquid is ' P ' at a point where flow speed is ' $v$ ', then pressure at another point where the flow of speed becomes 3 v is

An ideal fluid is flowing in a non-uniform cross-sectional tube $XY$ (as shown in the figure) from end $X$ to end $Y$. If $K_1$ and $K_2$ are the kinetic energy per unit volume of the fluid at $X$ and $Y$ respectively, then the correct option is:

Glycerine of density $1.25 \times 10^{3}\text{ kg/m}^3$ is flowing in conical shaped horizontal pipe. Crosssectional area of the pipe at its both ends is $10\text{ cm}^2$ and $5\text{ cm}^2$ respectively. Pressure difference at both the ends is $3\text{ N/m}^2$. Rate of flow of liquid in the pipe is

Water is flowing through a horizontal pipe in stream line flow. At the narrowest part of the pipe

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $A$ is $1.5\text{ cm}^2$, and $B$ is $25\text{ mm}^2$, if the speed of liquid at $B$ is $60\text{ cm/s}$ then $(P_A - P_B)$ is:

(Given $P_A$ and $P_B$ are liquid pressures at $A$ and $B$ points.

density $\rho = 1000\text{ kg m}^{-3}$

$A$ and $B$ are on the axis of tube

Glycerin of density $1.25 \times 10^{3}\text{ kg m}^{-3}$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are $10\text{ cm}^2$ and $5\text{ cm}^2$ and pressure drop across its length is $3\text{ Nm}^{-2}$. The rate of flow of glycerin through the pipe is $x \times 10^{-5}\text{ m}^3\text{ s}^{-1}$. The value of $x$ is ___________.

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0\text{ cm}^2$. The area of cross section at the outlet is $10\text{ mm}^2$. If the piston is pushed at a speed of $4\text{ cm s}^{-1}$, the speed of outgoing fluid is __________ $\text{cms}^{-1}$

A liquid of density 750 kgm${}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross- sectional area from A1 = 1.2 $\times$ 10$-$2 m2 to A2 = $\frac{A_1}{2}$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ $\times$ 10$-$3 m3s${}^{-1}$.

An ideal fluid of density 800 kgm${}^{-3}$, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $\frac{a}{2}$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $\frac{\sqrt{x}}{6}$ ms${}^{-1}$ for x = ___________. (Given g = 10 ms${}^{-2}$)

A tube of length $50\text{ cm}$ is filled completely with an incompressible liquid of mass $250\text{ g}$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $x\sqrt{F}\text{ rad s}^{-1}$. If $F$ be the force exerted by the liquid at the other end then the value of $x$ will be __________.

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 pascal. At another point where pressure is $\frac{P}{2}$ Pascal its speed is V ms–1. If the density of the fluid is $\rho$ kg m–3 and the flow is streamline, then V is equal to:

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 cm2 and 20 cm2, respectively. Find the

rate of flow of water through the tube.

(density of water = 1000 kgm–3)

A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?