Water having a density of 1000 kg/m^3 is flowing with a velocity of 3 m/s through a round pipe. There is a restriction within the pipe where the diameter is one-half the normal diameter. Determine the water velocity at the restriction.

12 m/s

Explanation:

Using the continuity equation, which is an extension of the conservation of mass law

ρ₁A₁v₁ = ρ₂A₂v₂

where 1 and 2 indicate the conditions at two different points of flow, in this case, point 1 is any normal position in the pip and point 2 is the conditions at the restriction.

ρ = density of the fluid flowing; note that the density of the fluid flowing (water) is constant all through the fluid's flow

A₁ = Cross sectional Area of the pipe at point 1 = (πD₁²/4)

A₂ = Cross sectional Area of the pipe at the restriction = (πD₂²/4)

v₁ = velocity of the fluid flowing at point 1 = 3 m/s

v₂ = velocity of the fluid flowing at The restriction = ?

ρ₁A₁v₁ = ρ₂A₂v₂

Becomes

A₁v₁ = A₂v₂ (since ρ₁ = ρ₂)

(πD₁²/4) × 3 = (πD₂²/4) × v₂

3D₁² = D₂² × v₂

But

D₂ = (D₁/2)

And D₂² = (D₁²/4)

3D₁² = D₂² × v₂

3D₁² = (D₁²/4) × v₂

(D₁²/4) × v₂ = 3D₁²

v₂ = 4×3 = 12 m/s

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

answer;

d. are made mostly of liquid

explanation;

-the general   composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.