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)

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation:

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get