To what height should a cylindrical vessel be filled with a homogenous liquid to make the force with which the liquid presses the side of the vessel becomes equal to the force exerted by the liquid on the bottom of the vessel? Given: \(r\) is the radius of the cylindrical vessel.
Ans: \(h=r\)
A water tank of square cross-section \(\left(l\times l\right)\) is filled with water up to a height \(h\). What is the thrust at (i) Bottom face of tank. (ii) Vertical face?
Ans:(i) \(\rho ghl^{2}\) and \(\left(\rho g\frac{h}{2}\right)\times hl\).
A container has a length of one meter. It is filled with three immiscible liquid A,B and C of densities \(1000\frac{kg}{m^{3}}\), \(1100\frac{kg}{m^{3}}\) and \(900\frac{kg}{m^{3}}\) respectively. If the liquid A and B have heights \(0.3\,m\) and \(0.2\,m\) respectively. Find: the pressure acting on the base of the container. Given: atmospheric pressure is \(\left(1.013\times10^{3}\right)\frac{N}{m^{2}}\).
A liquid is filled in a conical bucket having radii a and b of its lower and upper cross-sections respectively. If \(\rho\) be the density of the liquid and \(h\) is the height of bucket. Find: the net downward thrust on the inclined surface of the bucket?
Ans: \(F_{v}=\frac{1}{3}\pi\rho gh(b-a)(b+2a)\).
Consider a double-fluid manometer attached to an air pipe as shown in below figure. If the specific gravity of the one liquid is \(13.5\). determine the specific gravity of the outer fluid for the indicated absolutely pressure of air. Take: the atmospheric pressure to be \(\left(1\times10^{5}\right)Pa\).
Ans: \(R.D=1.046\).
A cubical block of steel has each side \(20\,cm\). The density of steel is \(7.8\frac{g}{cm^{3}}\). If floats on the surface of mercury contained in a vessel with its sides vertical. If the density of mercury is \(13600\frac{kg}{m^{3}}\). Then: (i) Find: the length of the block above the surface of mercury? (ii) If the water is poured on mercury surface in the container. Find: the height of water column when water just covers the top of the cubical block.
Ans:(i) \(l_{1}=8.53\,cm\) and (ii) \(l_{2}=9.2\,cm\).
