Question

1) A 40-m vertical column of fluid with density of 1872 kg/m3 is located where g = 9.65 g/m2. Find the pressure at the base of the column.

2) Two liquids of different densities (ρ1 = 1500 kg/m3 , ρ2 = 500 kg/m3) are poured together into a 120-liter tank, filling it. If the resulting density of the mixture is 820 kg/m3, find the respective amounts of liquids used. Also find the weight of the mixture; local g= 9.675 m/s2.

3) If a pump discharges 284 liters per minute of water whose density is 985 kg/m3, find (a)the mass flow rate in kg/min, (b) the total time required to fill a vertical tank 3 m in diameter and 4 m high.

6)Fahrenheit and a Celsius thermometer are both immersed in a fluid and indicate identical numerical readings. What is the temperature of the fluid expressed as °R and as °K?

Answer 1

$1)\ h = 40\ m\\\rho = 1872\ kg/m³\\ g = 9.65\ m/s²$

$P = \rho gh = 1872× 9.65×40 = 722592 Pa$

$2)\ \rho_1 = 1500\ kg/m³\\ \rho_2 = 500\ kg/m³\\ V = 120\ L\\ \rho_r = 820\ kg/m³\\ g = 9.675\ m/s²$

$\rho = m/V\\ m_r = 820 × 120 = 98400\ kg\\ 1500x + 500(120-x)= 98400\\ 1500x + 60000- 500x = 98400\\ 1000x = 38400\\ x = 38.4\ L$

$\therefore$ 38.4 L of the first liquid is used and 81.6 L of the second liquid is used.

$3)\ V/t= 284\ L\ per\ minute\\ \rho = 985\ kg/m³\\$

$(a)\ m/t = V/t ×\rho= 284× 985 =279740\ kg/min\\ (b) \ V = πr²h = π(3/2)²× 4 = 28.27m³\\ m = 28.27 ×985 = 27846\ kg\\ t = 27846/279740 = 0.0995\ min = 5.97\ sec$

6)\The Fahrenheit and Celsius scales have one point at which they intersect. They are equal at -40 °C and -40 °F

$K = °C + 273.15 = -40+ 273.15= 233.15K\\ °R = °F + 459.67= -40+ 459.67 = 419.67°R$