Atank is full of oil weighing 30 lb/ft3. the tank is a right rectangular prism with a width of 2 feet, a depth of 2 feet, and a height of 3 feet. find the work required to pump the water to a height of 2 feet above the top of the tank

the work will be W= 17373.96 lb*ft²/s²

Step-by-step explanation:

Neglecting the frictional losses in the pipe and the pump efficiency, then assuming a reversible process the work W will be

W= ∫pdV

from an energy balance (see note below), and assuming constant density of the oil, the pressures at pump output and pump input will be

P final = p₀ + ρ*g*h = p₀ + ρ*g*h + 1/2ρ*v²

P initial =  p₀ + 1/2ρ*v²

where

p₀= pressure at the surface

ρ= density

g= gravity

h= height of the oil level

the volume of pumped oil will be

V= A*h

dV=A*dh

then the pressure the pump has to work against is:

p= Pfinal- Pinitial = ρ*g*h

therefore

W=∫pdV = A∫ρ*g*h*dh = A*ρ*g*H²/2 = ρ*g*V*H/2

replacing values

V= 2 ft* 2 ft * 3 ft = 12 ft³

W= ρ*g*V*H/2= 30 lb/ft³* 32.174 ft/s²* 12 ft³ * 3 ft/2 = 17373.96 lb*ft²/s²

W= 17373.96 lb*ft²/s²

Note

- from mass conservation at the bottom of the tank and pump output

Apipe*vpipe = Apump*vpump

assuming that the discharge pipe has the same pipe diameter then Apump= Apipe → vpipe= vpump=v

- the final work is the average of the work for a completely charged tank and with almost any oil (H=0)  ( assuming no suction of air/vapor with low oil levels)

so then what are you asking?

step-by-step explanation:

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.