Sheet 02 Pascal’s Law, Hydraulic Machine, Hydrostatic Paradox and Manometer.
A car of mass \(800kg\) is lifted by a hydraulic lift. The radius of larger and smaller piston are \(1\,m\) and \(0.2\,m\) respectively. Calculate: the force exerted on the smaller piston to lift the car. If, the force is applied by the weight of man sitting on the smaller piston, what is his mass?
Ans: \(m=32\,kg\).
In a car lift, compressed air exerts a force \(F_{1}\) on a smaller piston having a radius of \(5.0\,cm\). This pressure is transmitted to a second piston of radius \(15cm\). If, the mass of the car to be lifted is \(1350\,kg\). Calculate: \(F_{1}\). What is the pressure necessary to accomplish this task? Take: \(g=9.8\frac{m}{s^{2}}\).
Ans: \(F_{1}=1470\,N\) and \(P=\left(1.9\times10^{5}\right)Pa\).
Two syringes of different cross-section (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of smaller piston and larger piston are \(1.0\,cm\) and \(3.0\,cm\) respectively. (a) Find: The force exerted on the larger piston when a force of \(10N\) is applied to the smaller piston. (b) If the smaller piston is pushed in through \(6.0\,cm\), how much does the larger piston move out?
Ans:(a) \(F_{2}=90N\) and (b) \(L_{2}=0.67\,cm\).
Two piston of hydraulic press have diameters of \(30.0\,cm\) and \(2.5\,cm\). Find: the force exerted by the longer piston when \(50\,kg-wt\) is placed on the smaller piston. If, the stroke of the smaller piston is \(4\,cm\). Find: the distance through which the longer piston will move after \(10\) strokes.
Ans: \(2.78\,mm\).
A hydraulic lift has two pistons A and B of cross-sectional area \(F_{1}\) and \(F_{2}\) are acting on them respectively. If, the force on the piston A is doubled and area of piston B is reduced to one-third. Find: the new force on piston B. Given: that the original force on it was \(30\,N\) .
Ans: \(20\,N\).
The neck and the bottom of a glass bottle are \(2.5\,cm\) and \(20\,cm\) in diameter respectively. A cork is pressed at the neck of the bottle with a force of \(1.5\,kgf\). Find: the force exerted at the bottom of the bottle.
Ans: \(96\,kgf\).
The atmospheric pressure at a place is \(1\,atm\). Express it in (a) C.G.S Units. and (b) S.I Units.
Ans:(a) \(1\,atm=\left(1.0129\times10^{6}\right)\frac{dyne}{cm^{2}}\). and (b) \(1\,atm=\left(1.0129\times10^{5}\right)Pa\).
What is the pressure on a swimmer \(10\,m\) below the surface of a fresh water lake?
Ans: \(P=\left(1.99\times10^{5}\right)Pa\).
If, water is being used as barometric liquid. What would be the height of the water column at standard atmospheric pressure. Given: Standard atmospheric pressure is \(76\,cm\) of mercury column and the density of the mercury is \(\rho_{Hg}=13.6\frac{g}{cm^{3}}\).
Ans: \(h_{water}=10.33\,m\).
Atmospheric pressure at a place is \(72\,cm\) of mercury column. If, the barometer tube is inclined at an angle of \(60^{o}\) with the horizontal. Find: the length of the mercury column in the tube.
Ans: \(l=83.14\,cm\).
At a depth of \(1000\,m\) in an ocean (a) What is the the absolute pressure? (b) What is the gauge pressure? (c) Find: the force acting on the window of area \(20\,cm\times20\,cm\) of a submarine at this depth, the interior of which is maintained at sea-level atmospheric pressure. [The density of sea water is \(\rho_{sea\,water}=\left(1.03\times10^{3}\right)\frac{kg}{m^{3}}\) , and \(g=10\frac{m}{s^{2}}\).
The L-shaped tank shown in the below figure is filled with water and is open at the top. If, \(a=6\,m\), Find: the the force due to the water (a) On face I? and (b) On face II? Taking: \(g=10\frac{m}{s^{2}}\).
A U-tube has its arms open to atmosphere. Water is filled into one arm and a light oil into other arm. One arm contain water up to a height of \(10\,cm\) whereas the other arm contains both water and oil. The oil to water ration in this arm is \(\frac{6}{1}\). If, the specific gravity of the oil is \(0.79\). Determine: The height of the each fluid in the other arm?
Ans: \(h_{water}=12.2\,cm\) and \(h_{oil}=73.2\,cm\).
A U-tube contains a liquid is accelerated horizontally with a constant acceleration \(a\). The separation between two vertical arms of the U-tube is \(L\). Find: the difference in height of the liquid in the two arms?
Ans: \(h=\frac{L.a}{g}\).
A spherical container with a long neck contains a liquid with density \(\left(1.1\times10^{3}\right)\frac{kg}{m6{3}}\). The length of the long neck is \(40\,cm\) and the radius of the spherical container is \(5\,cm\). Find: the pressure of the liquid at the base of the container. What is the absolute pressure at the base? If, the atmospheric pressure is \(10^{5}Pa\).
A column of water \(40\,cm\) height supports a \(50\,cm\) column if oil. Find: the density of the oil?
Ans: \(\rho_{oil}=800\frac{kg}{m^{3}}\).
A gauge pressure \(32\,psi\) is generally maintained for air in a car tyre. What is the absolute pressure? Given: \(1\,psi=\left(6.895\times10^{3}\right)Pa\).
A manometer is used to measure the pressure of a gas in a tank. The fluid used has a specific gravity of \(0.85\). If, the atmospheric pressure is \(100\,kPa\) and manometer height is \(55\,cm\) as shown in figure. Find: (a) the absolute pressure within the tank. And (b) The gauge pressure.
Ans: \(P_{absolute}=104.58\,kPa\) and \(P_{gauge}=4.58\,kPa\).
