Answer to Question #102221 in Mechanics | Relativity for Nyx

Question #102221
A horizontal pipe of diameter 1.09 m has a
smooth constriction to a section of diameter
0.654 m . The density of oil flowing in the pipe
is 821 kg/m3.
If the pressure in the pipe is 7190 N/m2
and in the constricted section is 5392.5 N/m2,
what is the rate at which oil is flowing?
Answer in units of m3/s.
Don't round answer
1
Expert's answer
2020-02-07T10:34:26-0500

For an in-compressible liquid:


"A_1v_1=A_2v_2"

"P_1+0.5\\rho v_1^2=P_2+0.5\\rho v_2^2"

"\\frac{v_2}{v_1}=\\frac{d_1^2}{d_2^2}=\\frac{1.09^2}{0.654^2}=2.778"

"7190+0.5(821) v_1^2=5392.5+0.5(821)(2.778)^2 v_1^2"

"v_1=0.8074\\frac{m}{s}"

So,


"Q=0.25\\pi d_1^2v_1"

"Q=0.25\\pi (1.09)^2(0.8074)=0.753\\frac{m^3}{s}"


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