Fluid Flow & Continuity Equation Video Lessons

Concept

# Problem: Water flows through a water hose at a rate of Q1 = 620 cm3/s, the diameter of the hose is d1 = 2.48 cm. A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of v2 = 14.8 m/s.a. Enter an expression for the cross-sectional area of the hose, A1, in terms of its diameter, d1.  A1 =b. Calculate the numerical value of A1, in square centimeters.A1 =c. Enter an expression for the speed of the water in the hose, v1, in terms of the volume flow rate Q1 and cross-sectional area A1.v1 =d.Calculate the speed of the water in the hose, v1 in meters per second.v1 =e.Enter an expression for the cross-sectional area of the nozzle, A2, in terms of v1, v2 and A1.A2 =f. Calculate the cross-sectional area of the nozzle, A2 in square centimeters.A2 =

###### FREE Expert Solution

Flow rate:

$\overline{){\mathbf{Q}}{\mathbf{=}}{\mathbf{A}}{\mathbf{v}}}$

Where Q is the flow rate, A is the cross-sectional area, and v is the velocity.

(a)

A1 = πr12 = (πd12)/4

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###### Problem Details

Water flows through a water hose at a rate of Q1 = 620 cm3/s, the diameter of the hose is d1 = 2.48 cm. A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of v2 = 14.8 m/s.

a. Enter an expression for the cross-sectional area of the hose, A1, in terms of its diameter, d1.

A1 =

b. Calculate the numerical value of A1, in square centimeters.

A1 =

c. Enter an expression for the speed of the water in the hose, v1, in terms of the volume flow rate Q1 and cross-sectional area A1.

v1 =

d.Calculate the speed of the water in the hose, v1 in meters per second.

v1 =

e.Enter an expression for the cross-sectional area of the nozzle, A2, in terms of v1, v2 and A1.

A2 =

f. Calculate the cross-sectional area of the nozzle, A2 in square centimeters.

A2 =