A horizontal pipe (Venturi Tube) 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 5.0 x 105 Pa and the pressure in the smaller pipe is 4.0 x 104 Pa, at what rate does water flow through the pipes. Hint: Use the continuity equation to express one speed in terms of the another.

Name: A horizontal pipe (Venturi Tube) 10.0 cm in diameter has a smooth redu
Uploaded: 2024-03-20T06:51:10.000Z
Channel: Bartleby
Description: A horizontal pipe (Venturi Tube) 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 5.0 x 105 Pa and the pressure in the smaller pipe is 4.0 x 104 Pa, at what rate does

Given data The first diameter is d1=10.0 cm The second diameter is d2=5.00 cm The first pressure is P1=5.0×105 Pa The second pressure is P2=4.0×104 Pa As the discharge is the same on both side of the pipe, Q1=Q2A1v1=A2v2π4d21v1=π4d22v2d21v1=d22v2 Here Q1 is the initial discharge of the pipe. Q2 is the final discharge of the pipe. v1 is the initial velocity of the pipe. v2 is the final velocity of the pipe.Substitute the given values, d21v1=d22v210×10-2 m2v1=5×10-2 m2v2v2=10×10-2 m2v15×10-2 m2=4v1 The Bernoulli's equation for the initial and final part of the pipe is, P1+12ρv21+z1=P2+12ρv22+z2 Here ρ is the density of water. z1=z2=z are datum level of each side of the pipe.Substitute the given values, P1+12ρv21+z1=P2+12ρv22+z25.0×105 Pa+121000 kg/m3v21+z=4.0×104 Pa+121000 kg/m34v12+z10.0×105 Pa+1000 kg/m3v21=8.0×104 Pa+16000 kg/m3v21920000 Pa=16000 kg/m3-1000 kg/m3v21v1=920000 Pa16000 kg/m3-1000 kg/m3=7.83 m/s The rate of the water flowing through the pipe is Q1=A1v1=π4d21v1=π410×10-2 m27.83 m/s=0.0615 m3/s Thus, the mass flow rate of the water flowing through the pipe is 0.0615 m3/s.