Answer to Question #195905 in Physics for Desiree

Question

what flows steadily through a pipe at the rate of 64 ft^3/min. A pressure gauge placed on a section of the pipe where the diameter is 40 in reads16lb/in^2 .Determine the pressure in the section of the pipe where the diameter is constricted to 2.0 in 

Answer 1

$64\ (ft^3/min)=0.03\ (m^3/s)$

$40\ (in)=1.016\ (m)$

$2 \ (in)=0.0508\ (m)$

$16\ (lb/in^2)=110316\ (Pa)$

$v_1=Q/(\pi d_1)=0.03/(3.14\cdot1.016)=0.0094\ (m/s)$

$v_2=Q/(\pi d_2)=0.03/(3.14\cdot0.0508)=0.188\ (m/s)$

$\rho v_1^2/2+p_1=\rho v_2^2/2+p_2\to p_2=\rho v_1^2/2+p_1-\rho v_2^2/2=$

$=1000\cdot 0.0094^2/2+110316-1000\cdot 0.188^2/2=$

$=110298\ (Pa)=15.997\ (lb/in^2)$ . Answer