Water is in streamline flow along a horizontal pipe with nonuniform cross-section. At a point in the pipe where the area of cross-section is 10 cm2, the velocity of water is 1 ms-1 and the pressure is 2000 Pa. The pressure at another point where the cross sectional area is 5 cm2 is...........

Question

Water is in streamline flow along a horizontal pipe with nonuniform cross-section. At a point in the pipe where the area of cross-section is 10 cm2, the velocity of water is 1 ms-1 and the pressure is 2000 Pa. The pressure at another point where the cross sectional area is 5 cm2 is........... (A) 1000 Pa (B) 500 Pa (C) 4000 Pa (D) 2000 Pa

Tardigrade Admin · Accepted Answer

According to equation of continuity A1 v1 =A2 v2 10 × 1 =5 × v2 v2 =2 m / s (p1/ρ)+(v12/2) =(p2/ρ)+(v22/2) (2000/1000)+(12/2) =(p2/1000)+(22/2) p2 =500 Pa

Q. Water is in streamline flow along a horizontal pipe with nonuniform cross-section. At a point in the pipe where the area of cross-section is 10cm2, the velocity of water is 1 ms−1 and the pressure is 2000Pa. The pressure at another point where the cross sectional area is 5cm2 is...........

1000 Pa

500 Pa

4000 Pa

2000 Pa

According to equation of continuity A1​v1​=A2​v2​ 10×1=5×v2​ v2​=2m/s ρp1​​+2v12​​=ρp2​​+2v22​​ 10002000​+212​=1000p2​​+222​ p2​=500Pa

According to equation of continuity
$A_{1} v_{1} = A_{2} v_{2}$
$10 \times 1 = 5 \times v_{2}$
$v_{2} = 2 m / s$
$\frac{p _{1}}{ρ} + \frac{v _{1}^{2}}{2} = \frac{p _{2}}{ρ} + \frac{v _{2}^{2}}{2}$
$\frac{2000}{1000} + \frac{1 ^{2}}{2} = \frac{p _{2}}{1000} + \frac{2 ^{2}}{2}$
$p_{2} = 500 P a$