Find the P1SolutionSolution Given data D1100 mm 01m P2 1 at

Solution

Solution

Given data

D1=100 mm = 0.1m

P2= 1 atm = 1 x 10^5 N/m2

D2= 50mm =0.05 m

Q= 2000   L/min = 0.03333333 m3/sec

To find

P1

Solution

A1 = (3.14/4) *D1^2 = 0.785*0.1^2 = 0.00785 m^2

V1= Q/A1 = 0.03333/0.00785 = 4.245 m/s

A2 = (3.14/4) * D2^2 = 0.785*0.05^2 = 0.0019625 m^2

V2=Q/A2 = 0.03333/0.0019625 = 16.983 m/s

From Bernoulli equation

P1-P2 = ½ *rao*(V2^2-V1^2)

P1= P2 + ½ *rao*(V2^2-V1^2)

     = 1 x10^5 + (1/2 * 1000* (16.983^2- 4.245^2)

    P1 = 2.3430 x10^5 N/m^2 = 2.343 bar