brine solution with density of 1230 kg/m³ moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is P₁ = 2.00 x 104 Pa, and the pipe iameter is 5.00 cm. At another point y = 0.40 m higher, the pressure is P₂ = 1.00 x 104 Pa and the pipe diameter is 2.50 cm. (a) Find the speed of flow (in m/s) in the lower section. 1.72 Write Bernoulli's equation for this situation. Use the continuity equation to express v₁ in terms of V₂. Combine Bernoulli's equation and the equation of continuity to determine the desired speed. m/s (b) Find the speed of flow (in m/s) in the upper section. * You determine v₁ in part (a). Use the equation of continuity to express v₂ in terms of v₁ and the diameter (or the radius) of the pipe at both ends. m/s (c) Find the volume flow rate (in m³/s) through the pipe. X The volume flow rate at any point in the pipe may be expressed in terms of the speed and radius (or diameter) of the pipe at that point. If the pipe is filled with a fluid, should the volume flow

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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Chapter15: Fluids
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A brine solution with a density of 1230 kg/m³ moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is P₁ = 2.00 × 104 Pa, and the pipe
diameter is 5.00 cm. At another point y = 0.40 m higher, the pressure is P2 = 1.00 × 104 Pa and the pipe diameter is 2.50 cm.
P₁
(a) Find the speed of flow (in m/s) in the lower section.
1.72
Write Bernoulli's equation for this situation. Use the continuity equation to express v₁ in terms of V₂. Combine Bernoulli's equation and the equation of continuity to determine the desired speed.
m/s
(b) Find the speed of flow (in m/s) in the upper section.
You determine v₁ in part (a). Use the equation of continuity to express V₂ in terms of V₁ and the diameter (or the radius) of the pipe at both ends. m/s
(c) Find the volume flow rate (in m³/s) through the pipe.
X
The volume flow rate at any point in the pipe may be expressed in terms of the speed and radius (or diameter) of the pipe at that point. If the pipe is filled with a fluid, should the volume flow
rate be the same or different at each point in the pipe? m³/s
Transcribed Image Text:A brine solution with a density of 1230 kg/m³ moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is P₁ = 2.00 × 104 Pa, and the pipe diameter is 5.00 cm. At another point y = 0.40 m higher, the pressure is P2 = 1.00 × 104 Pa and the pipe diameter is 2.50 cm. P₁ (a) Find the speed of flow (in m/s) in the lower section. 1.72 Write Bernoulli's equation for this situation. Use the continuity equation to express v₁ in terms of V₂. Combine Bernoulli's equation and the equation of continuity to determine the desired speed. m/s (b) Find the speed of flow (in m/s) in the upper section. You determine v₁ in part (a). Use the equation of continuity to express V₂ in terms of V₁ and the diameter (or the radius) of the pipe at both ends. m/s (c) Find the volume flow rate (in m³/s) through the pipe. X The volume flow rate at any point in the pipe may be expressed in terms of the speed and radius (or diameter) of the pipe at that point. If the pipe is filled with a fluid, should the volume flow rate be the same or different at each point in the pipe? m³/s
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