If water (p=998 kg/m", u = 10-3 pa. s) flows through a 50 mm-diameter pipe at 2 m/s, determine the velocity of carbon tetrachloride (p=1590 kg/mº, u=0.958 x 10-pa. s) flowing through a 60 mm-diameter pipe so that they both have the same dynamic characteristics (reynolds number similarity, repud/).

the velocity of carbon tetra chloride is 1.002 m/s

Explanation:

Given data

water density ρ = 998 kg/m

water viscosity μ  = 10³ Pa-s

pipe diameter D =  50 mm = 0.05 m

velocity of carbon v = 2 m/s

tetra chloride density ρ = 1590 kg/m

tetra chloride viscosity μ  = 0.958 x 10³ Pa-s

pipe diameter D =  60 mm = 0.06 m

to find out

the velocity of carbon tetra chloride

solution

we know here both of these are of same dynamic characteristics

so we say that

Reynolds number of water is equal to Reynolds number of tetra chloride

ρ(w) ×V(w)×D(w) / μ(w) =    ρ(ccl4) ×V(ccl4)×D(ccl4) / μ(ccl4)

put here all value we get V(ccl4)

V(ccl4) = 998 × 2 × 50 × 0.958 / ( 1590 × 60 )

V(ccl4) = 1.002

the velocity of carbon tetra chloride is 1.002 m/s

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).