Higher Engineering Mathematics, Sixth Edition

314 Higher Engineering Mathematics

2. The pressurepand volumevof a mass of gas
   are related by the equationpv=50. If the pres-
   sure increases from 25.0 to 25.4, determine the
   approximate change in the volume of the gas.
   Find also the percentage change in the volume
   of the gas. [−0.032,−1.6%]


3. Determine the approximate increase in (a) the
   volume, and (b) the surface area of a cube
   of sidexcm ifxincreases from 20.0cm to
   20.05cm. [(a) 60cm^3 (b) 12cm^2 ]


4. The radius of a sphere decreases from 6.0cm
   to 5.96cm. Determine the approximate change
   in (a) the surface area, and (b) the volume.
   [(a)−6.03cm^2 (b)−18.10cm^3 ]
   5. The rate of flow of a liquid through a
   tube is given by Poiseuilles’s equation as:

Q=

pπr^4

8 ηL

where Qis the rate of flow, p

is the pressure difference between the ends

of the tube,ris the radius of the tube,L

is the length of the tube andηis the coeffi-

cient of viscosity of the liquid.ηis obtained

by measuring Q,p,r andL.IfQ can be

measured accurate to±0.5%,paccurate to

±3%,raccurate to±2% andLaccurate to

±1%, calculate the maximum possible per-

centage error in the value ofη.

[12.5%]