(Solved): Gasoline with a density of = 737 kg/m3 moves through a constricted pipe in steady, ideal flow. ...

Gasoline with a density of ???? = 737 kg/m³ moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is

P₁ = 1.90 ✕ 10⁴ Pa,

and the pipe diameter is d₁ = 7.00 cm. At another point

h = 0.20 m

higher, the pressure is

P₂ = 1.15 ✕ 10⁴ Pa

and the pipe diameter is d₂ = 2.92 cm.

A tube is open at both its left and right ends. The tube starts at the left end, extends horizontally to the right, curves up and to the right, and extends horizontally to the right again. The right end is higher than its left end, and the change in height is labeled y. The pressure at the left end is labeled P₁, and the pressure at the right end is labeled P₂.

(a)

Find the speed of flow (in m/s) in the lower section.

______ m/s

(b)

Find the speed of flow (in m/s) in the upper section.

______m/s

step 1:
Using Bernoulli's Equation, symbolically construct a relationship between the pressure, speed, and height of the fluid at points (1) and (2) in the pipe. Solve it for the difference in pressures (P₁ - P₂). Along with gravitational constant g, use the other symbolic quantities provided: ????, h, d₁, d₂, and unknowns v₁ and v₂.

P₁ - P₂ = ______

step 2:
Using the Equation of Continuity for Fluids, find the numerical factor between v₁ and v₂. (I'm going to name this factor "k", and I invite you to give it the same name for use in your algebraic path to the solution.)

v₂ = (k)v₁
v₂ = ( _____)v₁

step 3:
Substitute (k)v₁ in for v₂ in your equation from step 1, and solve for unknown value v₁. Once you have solved for v₁, use the relationship in step 2 to solve for v₂. Enter the answers in parts (a) and (b), above.

(c)

Find the volume flow rate (in m³/s) through the pipe.
(Note the definition of "flow rate" or "volume flux", as stated in "Relevant Concepts" at the beginning of the problem.)

________m³/s