1) Two oil vessels are taking oil from two hoses that have the same length but d

Question

1) Two oil vessels are taking oil from two hoses that have the same length but different radii and are connected to a main oil pipeline. If the radius ratio is R1/R2=1.70, what is the corresponding oil speed ratio v1/v2 in the two hoses?

2) Initially a balloon of radius 8.00 m is stationary in air with its load, including ballast that can be thrown out to raise the balloon. If the balloon and its load ascends 98.0 m in 10.0 s after releasing some ballast, what is the mass of the released ballast? Assume that the air density is 1.20 kg/m3.
Answer:

__________ kg.

3) Boeing 747 has a total effective wing area of 9.80

Explanation / Answer

same as pressure difference is constant for both the two.

so Av =Av

where A is their respective area of cross sections and v is the velocity of fluid

? r12 * v1 = ? r22 *v2

so   v1/v2 =[r2/r1]2

v1/v2 =[1/1.70]2

v1/v2 =0.3460

with ballast so that it remains stationary.in second after loosing ballast force of buoyancy

becomes greater than weight which provides it upward acceleration.

for first case,

FB =Mg + mg ......................................1

where M =mass of balloon

m=mass of ballast

for second case,

FB Mg =Ma ....................................2

as this balloon ascends 98.0 m in 10.0 sec,its acceleration will be

s=ut+0.5at2

98 =0+0.5*a*100

a=1.96 m/sec2

putting the value of FB from eq 1 to eq 2

Mg + mg Mg =Ma

mg=Ma

m =Ma/g

as FB =Vdg =25208.42 newton

so M=FB/g+a

M=2143.57 kg

so m=2143.57*1.96/9.8

m=428.71 kg

gravity.this problem can be solved using bernaulis equation

?P =0.5*?*[v2- v2]

      =0.5*1.20*[752- 602]

=1215 N/m2

so force acting upward on the plane =1215*9.80*100

F=1.190*106 newton

this force will balance the force of gravity

F=mg

m=1.215*105 kg

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