Water flows steadily through a horizontal pipe of varying cross section. At one place the pressure 15 1.5 atm and the speed is 1.0 m/sec. Determine the pressure at another place where the speed is 10 m/sec.
A. 0.5 atm
B. 0.6 atm
C. 0.7 atm
D. 0.8 atm
E, 1.0 atm

Respuesta :

Answer:

D. 1 atm

Explanation:

pressure P1 = 1.5 atm = 1.5 x 101325 = 151987.5 N/m^{2}

speed V = 1 m/s

speed U = 10 m/s

pressure P2 = ?

applying Bernoulli's equation we can find the pressure P2

[tex]\frac{1}{2}ρv^{2}+P1=\frac{1}{2}ρu^{2}+P2[/tex]

[tex]\frac{1}{2}ρv^{2}-\frac{1}{2}ρu^{2}+P1= P2[/tex]

[tex]P2=\frac{1}{2}ρ(v^{2}-u^{2})+P1[/tex]

where ρ is the density of water = 1000 kg/m^{3}

[tex]P2=\frac{1}{2}x1000x(1^{2}-10^{2})+151987.5 [/tex]

[tex]P2=\frac{1}{2}x1000x(-99)+151987.5[/tex]

P2 = 102487.7 N/m^{2}

P2 = 102487.7 / 101325 = 1.01 atm = 1 atm