Fluid mechanics (calculations) Flashcards
What must the pressure of a fluid be to enter a vein with gauge pressure 5000 Pa?
At least 5000 Pa above atmospheric pressure, so absolute pressure = 101325 Pa + 5000 Pa = 106325 Pa.
What is the buoyant force on an object in a fluid?
The weight of the fluid displaced by the object, B = rho_fluid * V_displaced * g.
Why must an IV bag be hung above the needle?
To create enough pressure (rho * g * h) to overcome the vein’s pressure.
In a U-tube, why are pressures equal at the same height in the same liquid?
Because the fluid is static, and pressure depends only on depth and density at that level.
If 1/4 of a raft’s thickness is above water when empty, what fraction is submerged?
3/4 of the raft’s thickness is submerged (1 - 1/4 = 3/4).
Calculate the minimum height h for fluid (rho = 1050 kg/m^3) to match 10000 Pa gauge pressure. (g = 9.8 m/s^2)
p = rho * g * h. 10000 = 1050 * 9.8 * h. h = 10000 / (1050 * 9.8) ≈ 0.97 m.
What’s the buoyant force on a 300 m^3 balloon in air (rho = 1.2 kg/m^3)? (g = 9.8 m/s^2)
B = rho * V * g = 1.2 * 300 * 9.8 = 3528 N.
In a U-tube, if h = 4 cm and rho = 1000 kg/m^3, what’s p_gas? (p_atm = 1.013 x 10^5 Pa, g = 9.8 m/s^2)
p_gas = p_atm + rho * g * h = 1.013 x 10^5 + 1000 * 9.8 * 0.04 = 1.0169 x 10^5 Pa.
If 1/3 of a raft’s thickness is above water empty, what’s the buoyant force relative to its weight?
B = 2/3 * m_raft * g, since 2/3 of the volume is submerged.
A 400 m^3 balloon (m = 446 kg) has B = 4822 N. What’s the net force? (g = 9.8 m/s^2)
W = 446 * 9.8 = 4370.8 N. F_net = B - W = 4822 - 4370.8 = 451.2 N upward.
What’s the minimum height h for fluid (rho = 950 kg/m^3) to match 10800 Pa gauge pressure? (g = 9.8 m/s^2)
p = rho * g * h. 10800 = 950 * 9.8 * h. h = 10800 / (950 * 9.8) ≈ 1.16 m.
A raft’s top is level with water when a 60 kg load is added. Empty, 1/3 is above water. What’s its mass? (rho_water = 1000 kg/m^3)
Empty: m_raft = 2/3 * rho_w * V. Loaded: m_raft + 60 = rho_w * V. Solve: m_raft = 120 kg.
Derive p_gas for a U-tube with liquid rho and height difference h.
p_gas = p_atm + rho * g * h, from equal pressures at the same liquid height.
A 446 kg balloon has B = 4822 N. What’s its acceleration? (g = 9.8 m/s^2)
F_net = 4822 - (446 * 9.8) = 451.2 N. a = F_net / m = 451.2 / 446 ≈ 1.01 m/s^2 upward.
A 140 kg raft has 1/3 above water empty. What’s its volume? (rho_water = 1000 kg/m^3)
B = m_raft * g = rho_w * (2/3 * V) * g. 140 = 1000 * (2/3 * V). V = 140 / (1000 * 2/3) = 0.21 m^3.
Fluid (rho = 1070 kg/m^3) needs 12000 Pa gauge pressure. What’s h if tube resistance adds 1000 Pa? (g = 9.8 m/s^2)
Total p = 12000 + 1000 = 13000 Pa. h = 13000 / (1070 * 9.8) ≈ 1.24 m.
A 500 m^3 balloon has m = 615 kg. What air density keeps it stationary? (g = 9.8 m/s^2)
B = W. rho_air * 500 * 9.8 = 615 * 9.8. rho_air = 615 / 500 = 1.23 kg/m^3.
A U-tube has oil (rho = 800 kg/m^3), h = 6 cm. What’s p_gas? (p_atm = 1.013 x 10^5 Pa, g = 9.8 m/s^2)
p_gas = p_atm + rho * g * h = 1.013 x 10^5 + 800 * 9.8 * 0.06 = 1.0177 x 10^5 Pa.
A 446 kg balloon (400 m^3) has B = 4700 N. What’s its acceleration? (g = 9.8 m/s^2)
W = 446 * 9.8 = 4370.8 N. F_net = 4700 - 4370.8 = 329.2 N up. a = 329.2 / 446 ≈ 0.74 m/s^2.
A 140 kg raft (V = 0.21 m^3) has 1/3 above water empty. What mass makes half submerged? (rho_water = 1000 kg/m^3)
B = rho_w * (0.5 * V) * g = 1000 * 0.105 * 9.8 = 1029 N. m_total = 1029 / 9.8 = 105 kg. m_load = 105 - 140 = -35 kg (needs adjustment).
A U-tube has water (rho = 1000 kg/m^3) and oil (rho = 900 kg/m^3), h_water = 5 cm. What’s p_gas? (p_atm = 1.013 x 10^5 Pa)
p_gas = p_atm + rho_w * g * h_w = 1.013 x 10^5 + 1000 * 9.8 * 0.05 = 1.0179 x 10^5 Pa.
Fluid (rho = 1070 kg/m^3) needs 10800 Pa gauge pressure, but bag top is at 0.9 x 10^5 Pa. What’s h? (g = 9.8 m/s^2)
p_tip = 0.9 x 10^5 + 10800 = 100800 Pa. p_top + rho * g * h = p_tip. h = (100800 - 0.9 x 10^5) / (1070 * 9.8) ≈ 1.03 m.
A 120 kg raft (V = 0.18 m^3) is 1/3 above water empty. What mass sinks it fully? (rho_water = 1000 kg/m^3)
B_max = rho_w * V * g = 1000 * 0.18 * 9.8 = 1764 N. m_total = 1764 / 9.8 = 180 kg. m_load = 180 - 120 = 60 kg.
A balloon (m = 400 kg) adjusts V to float in air (rho = 1.25 kg/m^3). What’s V? (g = 9.8 m/s^2)
B = W. rho * V * g = m * g. 1.25 * V * 9.8 = 400 * 9.8. V = 400 / 1.25 = 320 m^3.
A U-tube has water (rho = 1000 kg/m^3), h = 10 cm initially. Gas pressure doubles h. What’s p_gas? (p_atm = 1.013 x 10^5 Pa)
Initial: p_gas = 1.013 x 10^5 + 1000 * 9.8 * 0.1 = 1.023 x 10^5 Pa. New h = 0.2 m. p_gas_new = 1.013 x 10^5 + 1000 * 9.8 * 0.2 = 1.0326 x 10^5 Pa.
