Question

Suppose you have a 8.8cm diameter fire hose with a 3.2 cm diameter nozzle. Solve all questions: a and b!

Thank you.

Class Management | Help Assignment 8 Begin Date: 3/23/2020 9:01:00 AM -- Due Date: 3/30/2020 9:00:00 AM End Date: 3/30/2020 9:00:00 AM (8%) Problem 12: Suppose you have a 8.8 cm diameter fire hose with a 3.2 cm diameter nozzle. | A 50% Part (a) Calculate the pressure drop due to the Bernoulli effect as water enters the nozzle from the hose at the rate of 40.0 L/s. Take 1.00 103 kg/m” for the density of the water. Grade Summary P - P2= | Deductions 090 Potential 100% sin() cos t an() ( 7 8 9 HOME Submissions cotan asin() acoso E 4 5 6 Attempts remaining: 10 (2% per attempt) atan acotan sinh 1 2 3 detailed view cosh tanh cotanh0 + - 0 . END Degrees Radians VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 1% deduction per feedback. A 50% Part (b) To what maximum height, in meters, above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)

Answer 1

a)

Since flow rate is given by

Q=AV

Therefore

V1=Q/A1 = (40*10-3)/pi*0.0882/4 = 6.576650541 m/s

V2=Q/A2=(40*10-3)/pi*0.0322/4= 49.73591972 m/s

From Bernoulli's equation

P1 + (1/2)pV12 + pgh1 = P2 + (1/2)pV22 + pgh2

P1-P2 = (1/2)p(V22-V12) + pg(h2-h1)

P1-P2 =(1/2)(1000)(49.7362-6.5772)+1000*9.81*(h-h)

P1-P2 =1.2152*106 pa

b)

The Maximum height the water rise above the nozzle is

h=V22/2g =49.7362/2*9.81

h=126.08 m