Question

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?

Answer 1

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.$P=130N;$

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

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

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

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

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

$F_A=\rho_w gV;$

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

Answer: 1. $p=6.272\sdot10^6Pa;$

2.$p=54.527kPa;$

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

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