B M Sharma Solutions for Chapter: Fluid Mechanics, Exercise 1: DPP 4.1

A U-tube in which the cross-sectional area of the limb on the left is one-quarter, the limb on the right contains mercury (density $13.6\mathrm{ }\mathrm{g} {\mathrm{cm}}^{-3}$). The level of mercury in the narrow limb is at a distance of $36\mathrm{ }\mathrm{cm}$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?

Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel ($s=$relative density of mercury and $\rho =$density of water) by

An L-shaped glass tube is kept inside a bus that is moving with constant acceleration. During the motion, the level of the liquid in the left arm is at $12\mathrm{ }\mathrm{cm}$ whereas in the right arm, it is at $8\mathrm{ }\mathrm{cm}$ when the orientation of the tube is as shown. Assuming that the diameter of the tube is much smaller than levels of the liquid and neglecting effect of surface tension, acceleration of the bus will be ($\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2})$.

An open water tanker moving on a horizontal straight road has a cubical block of cork floating over its surface. If the tanker has an acceleration of $a$ as shown, the acceleration of the cork w.r.t. container is :

A $U$-tube of base length filled with the same volume of two liquids of densities $\rho$ and $2\rho$ is moving with an acceleration $a$ on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height $h$ is given by :

A broad vessel with a square base of edge $a=10 \mathrm{cm}$ is separated into two halves $A$ and $B$ by a smooth vertical piston. A spring of spring constant $\mathrm{k}=1500\mathrm{ }\mathrm{N} {\mathrm{m}}^{-1}$ is filled across the compartment $A$ and the compartment $B$ is filled with water to a height $20\mathrm{ }\mathrm{cm}.$ Find the compression in the spring.

A rectangular gate $3\mathrm{ }\mathrm{m}\times 1\mathrm{ }\mathrm{m}$ stands vertical with water on one side of it hinged at the middle. The force $F$ required to the applied at the bottom to keep the gate in equilibrium is 

Pressure is a scalar quantity because: