1-62 Determine the dimensions of c, », k, and P in the |differential equation d²x dx +c- dt + kx = P cos at in which m is mass, x is length, and t is time.
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Q: A special-purpose piece of laboratory glassware, called a pyncnometer; is used to measure Liquid…
A: Given: Volume , V = 25 cc=.025 LMass of pyncnometer with air = 17.24 gMass with liquid, m = 45.00 gm
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- A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:).Determine the dimensions of constants A and B far which the following equation is dimensionally homogeneous: F=Akx2sinBxk where F is a force, x is a distance, and k represents stiffness (dimensions: [FL1]).A differential equation is d2ydt2=Ay2+Byt where y represents a distance and t is time. Determine the dimensions of constants A and B for which the equation will be dimensionally homogeneous.
- 1. A special-purpose piece of laboratory glassware, called a pyncnometer; is used to measureLiquid densities. It has a volume of 25 cc, and a mass of 17 .24 g when it is full of air. Whenfilled with a liquid of unknown density, its mass = 45.00 g. What is the density of this liquid?How large an error do we make if we ignore the mass of the air that was in it when we weighed itand found m = 17.24 g?Determine the temperature of air in °C if the pressure is at 855 kPa and the specific volume is 0.1 m3/kg. Report your answer to nearest whole number using roundingᴀ ᴘᴜᴍᴘ ᴅᴇʟɪᴠᴇʀꜱ 0.3 ᴍ3/ꜱ ᴀɢᴀɪɴꜱᴛ ᴀ ʜᴇᴀᴅ ᴏꜰ 200 ᴍ ᴡɪᴛʜ ᴀ ꜱᴘᴇᴇᴅ ᴏꜰ 2000 ʀᴘᴍ. ꜰɪɴᴅ ᴛʜᴇ ꜱᴘᴇᴄɪꜰɪᴄ ꜱᴘᴇᴇᴅ
- A lubricating oil having the dynamic viscosity of 0.051 poise and specific gravity of 1.12. Calculate (i) the density of oil in kg/m3, (ii) the weight density of oil in N/m3,(iii) the kinematic viscosity in stokes, and (iv) the specific volume in m3/kg.At one point in a pipeline the water's speed is 3.00 m/sand the gauge pressure is 5.00×10^4 Pa a) Find the gauge pressure at a second point in the line, 11.0 mm lower than the first, if the pipe diameter at the second point is twice that at the first. Express your answer in kilopascals.(a). A lubricating oil having the dynamic viscosity of 0.055 poise and kinematic viscosity of 0.11 stokes. Calculate (i) the density of oil in kg/m³, (ii) the weight density of oil in N/m³, (i) the specific gravity, and (iv) the specific volume in m/kg.
- Evaluate the following to three significant figures and express each answer in SI units using an appropriate prefix: (684 mm)(43 ms)The sketch shows an oil manometer that is connected between two pipes which transport water. The density of water can be taken as 998kg/m3, the specific gravity of glycerol is 0.76 and atmospheric pressure is 100 kPa. The respective dimensions (as shown on the sketch) are given below: h1 = 0.17 m h2 = 350 mm h3 =15cm. From the given data, calculate the pressure difference between the two pipes.An engineer designing a light aircraft is trying to make an estimate of the diameter of the propeller needed. The design speed of the aircraft is 69m/s into still air and at this speed experience allows the engineer to assume a propeller efficiency of 88%. Other analysis shows that a thrust of 10906N must be supplied by the propeller to maintain this speed. Assuming a constant air density of 1.19 kg/m3 , determine the diameter of the ideal propeller in m to 1 decimal place.