When water falls from a tap, down the streamline area decreases due to increase in velocity of liquid as it experiences gravity, i.e., by equation of continuity.
$A_{1} v_{1}=A_{2} v_{2}$
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Water flows in a stream line manner through a capillary tube of radius $a$. The pressure difference being $P$ and the rate of flow is $Q$. If the radius is reduced to $\frac{a}{4}$ and the pressure is increased to $4 P$. then the rate of flow becomes ................
The Bhagirathi and the Alaknanda merge at Deoprayag to form the Ganga with their speeds in the ratio $1: 1: 5$. The cross-sectional areas of the Bhagirathi, the Alaknanda and the Ganga are in the ratio $1: 2: 3$. Assuming streamline flow, the ratio of the speed of Ganga to that of the Alaknanda is
An object is located at $2\, km$ beneath the surface of the water. If the fractional compression $\frac{\Delta V }{ V }$ is $1.36\, \%,$ the ratio of hydraulic stress to the corresponding hydraulic strain will be ......... . [Given : density of water is $1000\, kg m ^{-3}$ and $\left. g =9.8 \,ms ^{-2} .\right]$
The spring balance $A$ reads $2$ $kg$ with a block $m $ suspended from it. $A$ balance $B$ reads $5$ $kg$ when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation:
A cube of ice floats partly in water and partly in kerosene oil. The radio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $=0.8$, specific gravity of ice $=0.9$ )
A spherical solid ball of volume $V$ is made of a material of density $\rho_1$ . It is falling through a liquid of density $\rho_2 (\rho_2 < \rho_1 )$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous}= -kv^2 (k >0 )$,The terminal speed of the ball is
In the figure shown, a liquid is flowing through a tube at the rate of $0.1\, m^3/sec$. The tube is branched into two semicircular tubes of cross-sectional area $A/3$ and $2A/3$. The velocity of liquid at $Q$ is ......... $ m/sec$ (The cross-section of the main tube $= A =10^{-2}\, m^2$ and $v_p = 20\, m/sec$)
The bulk modulus of a liquid is $3 \times 10^{10}\, Nm ^{-2}$. The pressure required to reduce the volume of liquid by $2 \%$ is ........ $\times 10^{8}\; Nm ^{-2}$