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# Answer to Question #113370 in Engineering for Raphy

Question #113370
1. What gauge pressure in Pa must a pump produce in order to pump water from the bottom of Grand Canyon (730 m elevation) to the Indian gardens (1370 m)?

2. Calculate the pressure at the bottom of the container with 1.2 m high layer of oil (SG=0.82), 0.5 m layer of water and 0.3 m layer of mercury (SG=13.6)

3. A cube having a side 8 cm in length has a density of 900 kg/m³. What is the mass and unit weight of the cube?

4. Georgie is trying to float his toy boat on water during one rainy day. If it weighs 130 N and has a density of 9 g/cm³, what is the total volume of the toy and the buoyant force exerted on it?
1
2020-05-05T03:47:08-0400

Solution.

1."h_1=730m;"

"h_2=1370m;"

"p=\\rho g\\Delta h; \\Delta h=h_2-h_1;"

"\\Delta h=1370m-730m=640m;"

"p=1000kg\/m^3\\sdot9.8N\/kg\\sdot640m=6.272\\sdot10^6Pa;"

2."h_o=1.2m; \\rho_o=0.82g\/cm^3=820kg\/m^3;"

"h_w=0.5m; \\rho_w=1000kg\/m^3;"

"h_m=0.3m; \\rho_w=13.6g\/cm^3=13600kg\/m^3;"

"p=\\rho gh;"

"p_o=820kg\/m^3\\sdot 9.8N\/kg\\sdot1.2m=9643.2Pa=9.643kPa;"

"p_w=1000kg\/m^3\\sdot9.8N\/kg\\sdot0.5m=4900Pa=4.9kPa;"

"p_m=13600kg\/m^3\\sdot9.8N\/kg\\sdot0.3m=39984Pa=39.984kPa;"

"p=p_o+p_w+p_m;"

"p=9.643kPa+4.9kPa+39.984kPa=54.527kPa;"

3."a=8cm=0.08m;"

"\\rho=900kg\/m^3;"

"m=\\rho\\sdot V;"

"V=a^3;" "V=(0.08m)^3=0.000512m^3;"

"m=900kg\/m^3\\sdot0.000512m^3=0.4608kg;"

"P=mg; P=0.4608kg\\sdot9.8N\/kg=4.52N;"

4."P=130N;"

"\\rho=9g\/cm^3=9000kg\/m^3;"

"m=\\rho V \\implies V=\\dfrac{m}{\\rho};"

"P=mg\\implies m=\\dfrac{P}{g};"

"m=\\dfrac{130N}{9.8N\/kg}=13.265kg;"

"V=\\dfrac{13.265kg}{9000kg\/m^3}=0.00147m^3;"

"F_A=\\rho_w gV;"

"F_A=1000kg\/m^3\\sdot9.8N\/kg\\sdot0.00147m^3=14.4N;"

2."p=54.527kPa;"

3."m=0.4608kg;" "P=4.52N;"

4."V=0.00147m^3;" "F_A=14.4N;"

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